Free Printable linear equation in two variables class x

1.

On solving $\frac{25}{x+y}-\frac{3}{x-y}=1,\ \$ and $\frac{40}{x+y}+\frac{2}{x-y}=5\$ , we get

a)

$x=8,\ \ y=6$

b)

$x=4,\ \ y=6$

c)

$x=6,\ \ y=-4$

d)

None of these

2.

Solve $2x+3y=11$ and $2x-4y=-24$ and hence find the value of 'm' for which $y=mx+3$

a)

$m=1$

b)

$m=2$

c)

$m=-1$

d)

$m=-2$

3.

The path of a train A is given by the equation $x+2y-4=0$ and the path of another train B is given by the equation $2x+4y-12=0$ . Will the paths cross ? Solve by the method of substitution.

a)

$x=2,\ \ y=3$

b)

$x=-2,\ \ y=3$

c)

$x=-2,\ \ y=-3$

d)

None of these

4.

The equations $2x-3y+5=0$ and $6y-4x=10$ , when solved simultaneously, have :

a)

only one solution

b)

no solution

c)

only two solution

d)

infinite solution

5.

For what values of k will the following pair of linear equations have infinitely many solutions ? $kx+3y-\left(k-3\right)=0$ and $12x+ky-k=0$

a)

$k=-4$

b)

$k=6$

c)

$k=-3$

d)

$k=2$

6.

What is the solution to a system of equations?

a)

The point that the equations have in common.

b)

The point where the two lines intersect.

c)

All of the above.

7.

The pair of equations $ax+2y=7$ and $3x+by=16$ represent parallel lines if :

a)

$a=b$

b)

$2a-3b=0$

c)

$3a=2b$

d)

$ab=6$

8.

Solution of the system of equations $\sqrt{2}x-\sqrt{5}y=0$ and $\sqrt{5}x+\sqrt{2}y=0$ is

a)

$x=\sqrt{5},\ \ y=\sqrt{2}$

b)

$x=-\sqrt{2},\ \ y=\sqrt{5}$

c)

$x=0,\ \ y=0$

d)

$x=\sqrt{2},\ \ y=\sqrt{5}$

9.

The pair of equations $x=2$ and $y=3$ graphically represents lines which are :

a)

parallel

b)

intersecting at (2, 3 )

c)

intersecting at ( 3, 2 )

d)

coincident

10.

If a pair of linear equations is consistent, then the lines will be

a)

always parallel

b)

intersecting and coincident

c)

always intersecting

d)

always coincident

11.

Any point on the line x = y is of the form

a)

(k, -k)

b)

(0, k)

c)

(k, 0)

d)

(k, k)

12.

The linear equation 3x-11y=10 has

a)

Infinitely many solutions

b)

1 Solution

c)

Two solutions

d)

Unique solution

13.

Point (3, 4) lies on the graph of the equation 3y = kx + 7. The value of k is

a)

4/3

b)

3

c)

7/3

d)

5/3

14.

The equation y = 2 in two variables can be written as

a)

0 .x + 1 .y = 2

b)

1. x + 0. y = 2

c)

1. x + 0 .y = 0

15.

Solution of the equation 3x – 5 = 2x + 1is

a)

5

b)

7

c)

4

d)

6

16.

x = 4, y=3 is a solution of the linear equation

a)

2x + y = 17

b)

2x + 3y = 17

c)

x + 3y = 17

d)

2x+2y=17

17.

If the point (3, 4) lies on the graph of the equation 3y = ax + 7, then the value of a is

a)

3/5

b)

5/3

c)

3/7

d)

4/6

18.

The graph of linear equation x+2y = 2, cuts the y-axis at

a)

(2,0)

b)

(0,2)

c)

(0,1)

d)

(1,1)

19.

If 2x + 4 = x - 5, then x = ______

a)

9

b)

-9

c)

1

d)

-1

20.

the difference between two number is 40.

form a linear equation from above situation.

a)

x - y = 40

b)

x + y =40

c)

x = 40y

d)

y = 40x

21.

$x\ +4y=10$
identify whether the above equation are linear equation with two variables

a)

yes

b)

no

c)

not sure

22.

Find the solution of the given simultaneous equations.

y\ =\ 2x-3

3x-2y=4

a)

(2, 1)

b)

$\left(-\frac{7}{3},-\frac{23}{3}\right)$

c)

(-7, -17)

d)

(7, 4)

e)

no solution

23.

Find the solution of the given simultaneous equation.
$3x+2y=3$
$5x+3y=4$

a)

(-1,3)

b)

(17, -12)

c)

$\left(\frac{1}{2},\frac{3}{4}\right)$

d)

(-6, 3)

24.

Linear equation in one variable has

a)

Only one term with variable

b)

One variable with power >1

c)

More than one variable with any power

d)

One variable with power 1

25.

The value of x in 4x-7=17 is

a)

0.6

b)

6

c)

5

d)

6.6

26.

How many variables should be present in the given linear equation in able to consider as an example of Linear Equation in Two Variables?

a)

Four Different Variables

b)

Two Identical Variables

c)

Four Identical Variables

d)

Two Different Variables

27.

Which of the following is an example of Linear equation in Two Variables?

a)

x²- 25

b)

a³ - 27

c)

4x = 2y - 9

d)

x² + 3x + 2

28.

x + 20 = 100

a)

x = 80

b)

x = -5

c)

x = 20

d)

x = -80

29.

Solve for x:

a)

x = 20

b)

x = 7

c)

x = 10

d)

x = 3

30.

If (2 ,0) is a solution of the linear equation 2x + 3y = k, then the value of k is_____

a)

4

b)

5

c)

6

d)

2

31.

The graph of the linear equation 2x + 3y = 6 cuts the y - axis at the point _____

a)

(2 ,0)

b)

(0 ,3)

c)

(3 ,0)

d)

(0, 2)

32.

The graph of ax + by + c = 0 is _____

a)

A straight line parallel to x - axis

b)

A straight line parallel to y - axis

c)

A general straight line

d)

A line in the 2nd and 3rd quadrant

33.

The graph of the linear equation in two variables y = mx is _____

a)

a line parallel to x - axis

b)

a line parallel to y - axis

c)

a line passes through the origin

d)

not a straight line

34.

The point of the form (a , -a) always lies on the line____

a)

x = a

b)

y = - a

c)

y = x

d)

x + y = 0

35.

If 2x+3y = 12 and 3x-2y=5 then

a)

x = 2, y = 3

b)

x = 2, y = -3

c)

x = 3, y = 2

d)

x = 3, y = -2

36.

If a pair of linear equations is consistent then their graph lines will be_______

a)

Parallel

b)

Always coincident.

c)

Always intersecting.

d)

Intersecting or coincident.

37.

The pair of equation x+2y+5=0 and -3x-6y+1=0 has

a)

A unique solution

b)

Exactly two solutions

c)

Infinitely many solutions

d)

No solution.

38.

If the system of equations kx - 5y = 2, 6x + 2y = 7 has no solution, then k =___

a)

-10

b)

-5

c)

-6

d)

-15

39.

The value of k for which the system of equations 3x+5y=0 and kx+10y=0 have infinitely many solutions is _______

a)

0

b)

2

c)

6

d)

8

40.

If x+y=14 and x-y=4 then the values of x and y are_________

a)

x=4 and y = 5

b)

x = 9 and y = 7

c)

x = -6 and y = 5

d)

x = 9 and y = 5

41.

The system of equations kx - y = 2 and 6x - 2y = 3 has a unique solution only when k =_______

a)

0

b)

not equal to 0

c)

3

d)

not equal to 3

42.

If the lines given by 3x+2ky =2 and 2x+5y+1= 0 are parallel then the value of k is _______

a)

$\frac{-5}{4}$

b)

$\frac{2}{5}$

c)

$\frac{3}{2}$

d)

$\frac{15}{4}$

43.

The graphs of the equations 2x+3y-2=0 and x-2y-8=0 are two lines which are_______

a)

Coincident

b)

Parallel

c)

Intersecting exactly at one point

d)

Perpendicular to each other

44.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

Perpendicular lines

d)

coincident lines

45.

a)

Consistent : Unique solution

b)

Consistent: Many Solutions

c)

Inconsistent: No solution

d)

None of the above

46.

29x+37y=103 and 37x+29y = 95 then

a)

x=1, y=2

b)

x=2, y=1

c)

x=3, y=2

d)

x=2, y=3

47.

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?

a)

1/2

b)

−1/2

c)

2

d)

−2

48.

What is pair of linear equations in two variables?

a)

a set of two or more linear equations in the same two variables

b)

a polynomial with three terms

c)

set of two linear equations in same two variables

49.

If a system of linear equations has one solution, what does this mean about the two lines?

a)

Parallel lines

b)

the same line

c)

Intersecting lines

50.

How can you tell if a point is a solution to a system?

a)

It makes the first equation true.

b)

The (x,y) coordinates satisfy both equations

c)

It makes logical sense

d)

It makes neither equation negative

51.

If a pair of linear equations is consistent, then the lines will be

a)

parallel

b)

always coincident

c)

intersecting or coincident

d)

always intersecting

52.

The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is

a)

3

b)

– 3

c)

–12

d)

no value

53.

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is

a)

–5/4

b)

2/ 5

c)

15/4

d)

3/2

54.

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?

a)

1/2

b)

−1/2

c)

2

d)

−2

55.

The equations 4x + 3y – 1 = 5 and 12x + 9y = 15 represent

a)

No solution

b)

Infinite many solution

c)

Unique solution

56.

The equations 4x + 3y = 5 and 12x + 9y = 15 represent

a)

No solution

b)

Infinite many solution

c)

Unique solution

57.

A solution to a

system of linear equations

with two variables

is written as an ordered pair

( x, y ).

a)

True

b)

False

58.

For what values of a and b does the following pair of equations have an infinite numbers of solutions. 2x+3y=7, a(x+y)-b(x-y)=3a+b-2

a)

a = 5, b = - 1

b)

a = - 5, b = 5

c)

a = 5, b = 1

d)

a = 1, b = 5

59.

For what value of k will the following equations have infinitely many solutions? 2x-3y=7, (k+1) x+ (1-2k) y=5k-4

a)

1

b)

2

c)

3

d)

5

60.

For what value of k will pair of equations have no solution? 3x+y=1 , (2k-1)x+(k-1)y=2k+1

a)

1

b)

2

c)

3

d)

4

61.

^{What is the solution?}

a)

1

b)

-2

c)

(1, 2)

d)

(1, -1)

62.

Graphically, the pair of equations 6x – 3y + 10 = 0 , 2x – y + 9 = 0 represents two lines which are

a)

intersecting at exactly one point

b)

intersecting at exactly two points.

c)

coincident.

d)

parallel.

63.

The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have

a)

a unique solution

b)

exactly two solutions

c)

infinitely many solutions

d)

No solution

64.

If a pair of linear equations is consistent, then the lines will be

a)

parallel

b)

always coincident

c)

intersecting or coincident

d)

always intersecting

65.

The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is

a)

3

b)

– 3

c)

–12

d)

no value

66.

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is

a)

–5/4

b)

2/ 5

c)

15/4

d)

3/2

67.

The pair of equations x = a and y = b graphically represents lines which are

a)

parallel

b)

intersecting at (b, a)

c)

coincident

d)

intersecting at (a, b)

68.

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?

a)

1/2

b)

−1/2

c)

2

d)

−2

69.

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?

a)

1/2

b)

−1/2

c)

2

d)

−2

70.

The equations 4x + 3y – 1 = 5 and 12x + 9y = 15 represent

a)

No solution

b)

Infinite many solution

c)

Unique solution

71.

If 2x+3y = 12 and 3x-2y=5 then

a)

x = 2, y = 3

b)

x = 2, y = -3

c)

x = 3, y = 2

d)

x = 3, y = -2

72.

Solve

6x + y = + 5

-2x + y = 5

Find the value of y.

(a)

73.

Solve

y = -3x + 11

5x + y = 21

Find the value of x

(a)

74.

Solve

3x + y = 1

y = 4x + 1y

Find the value of y.

(a)

75.

Solve by elimination:

4x+9y=28

-4x-y=-28

Find the value of x

(a)

76.

Solve the system by multiplication.

3x + 2y = 16

7x + y = 19

a)

x= -2 , y= 5

b)

x= -2 , y= -5

c)

x= 2 , y= - 5

d)

x= 2 , y= 5

77.

Does the following system have One Solution, No Solution, or Infinite Solutions.

y = 4x + 8

y = -5x + 3

a)

One solution

b)

No solution

c)

Infinite solution

d)

many solutions

78.

Parallel lines have the same slope with a different y-intercept and how many solutions?

a)

One

b)

No

c)

Infinite

d)

Many

79.

Shreyas graphed two lines in order to find the solution to a given system of equations.Then the solution is......

a)

(-1, 4)

b)

(1, -4)

c)

(-4, 1)

d)

(4, -1)

80.

Solve for x and y

y = 2x + 1

y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

81.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

82.

What is the solution to the system?
8x + 4y = 12
y = -2x + 3

a)

(0,3)

b)

(3,0)

c)

No solution(parallel lines)

d)

Infinitely many solutions

83.

Which of the following are ways to solve systems of equations?

a)

Graphing

b)

Substitution

c)

Elimination

d)

All of the above

84.

Determine if (4, 1) is a solution for the system of equations.

y = -x + 5

y = 2x - 7

a)

yes

b)

no

c)

do not know

d)

may be

85.

Anjali finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. How long does it take her to do a haircut?

3x + 2y = 315

2x + 4y = 450

a)

45 minutes

b)

90 minutes

c)

60 minutes

d)

30 minutes

86.

Solve by the

Elimination method:

3x + y = -2

2x + y = 3

a)

(-5, 13)

b)

(13, 5)

c)

(5, -13)

d)

(-13,5)

87.

Solve the system by elimination.

−4x − 4y = 0

4x + 4y = 0

a)

(−6, −4)

b)

Infinite number of solutions

c)

(−6, 10)

d)

(6, 4)

88.

Solve the system of equations by substitution.
y = -4x + 5
y = 3x - 16

a)

(-3, -25)

b)

(3,-7)

c)

(11, 17)

d)

(21, 47)

89.

Which system of equations does NOT have the same solution as the system below?

3x\ +\ 5y\ =10

-x\ +4y\ =-3

a)

$30x\ +50\ y\ =100$
$-10x\ +\ 40y\ =-30$

b)

$18x\ +30y\ =60$
$-6x\ +24y\ =-18$

c)

$6x\ +\ 10y\ =\ 20$
$-3x\ +12y\ =-3$

d)

$-15x\ -25y\ =\ -50$
$-\frac{1}{2}x+2y\ =-\frac{3}{2}$

90.

How many solutions are there to the following system of equations?

y+2x=1

y+1=-2x

a)

One Solution

b)

No Solution

c)

Infinite Solutions

d)

Many solutions

91.

How do we know if a system of equations has no solution?

a)

The lines are not in slope-intercept form (y=mx+b)

b)

The lines have the same slope and y-intercept

c)

The lines are perpendicular

d)

The lines are parallel

92.

Which of these systems has an infinite number of solutions?

a)

y=-2x+1

y=-2x-3

b)

$y=3x+4$
$-12x+4y=16$

c)

$x+2y=10$
$2x+4y=10$

d)

$y=2x+6$
$4x-2y=8$

93.

Is (-1,5) a solution to this system of equations?

a)

$x+y=4$
$x=-1$

b)

$y=-x+4$
$y=-\frac{1}{5}x$

c)

$y=5$
$y=x-6$

d)

$y=x+6$
$x=2y+7$

94.

Graphically, the pair of equations 6x – 3y + 10 = 0 , 2x – y + 9 = 0 represents two lines which are

a)

intersecting at exactly one point

b)

intersecting at exactly two points.

c)

coincident.

d)

parallel.

95.

What is the solution(s) for the following intersection of two lines?

a)

(-1,-1)

b)

(-1,1)

c)

(1, 1)

d)

(1, -1)

96.

What will be the solution of these equations ax+by=a-b, bx-ay=a+b

a)

x=1, y=2

b)

x=2,y=-1

c)

x=-2, y=-2

d)

x=1, y=-1

97.

If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=4 then what will be value of a and b

a)

2,1

b)

3,1

c)

4,6

d)

1,2

98.

1. What is the solution for equations below?

y = 3x + 2

y = 5x

a)

x=2, y=8

b)

x=5, y=17

c)

x=1, y=5

d)

x= -2, y= -4

99.

The pair of equation x = – 4 and y = – 5 graphically represents lines which are

a)

intersecting at (-5, –4)

b)

intersecting at (-4, –5)

c)

intersecting at (5, 4)

d)

intersecting at (4, 5)

100.

The graph of the linear equation 2x +3y = 6 cuts the y-axis at the point:

a)

(2, 0)

b)

(0, 3)

c)

(3, 0)

d)

(0, 2)

101.

If x = a, y = b is the solution of the equations x + y = 5 and 2x – 3y = 4, then the values of a and b are respectively

a)

6, -1

b)

2, 3

c)

1,4

d)

19/5, 6/5

102.

The graph of x = -2 is a line parallel to the

a)

x-axis

b)

y-axis

c)

both x-axis and y-axis

d)

none of these

103.

If in the equation x + 2y = 10, the value of y is 6, then the value of x will be

a)

-2

b)

2

c)

3

d)

-3

104.

The pair of equations x = a and y = b graphically represents lines which are

a)

parallel

b)

intersecting at (b,a)

c)

coincident

d)

intersecting at (a,b)

105.

Find the value of k, if x = 1, y = 2 is a solution of the equation 2x + 3y = k.

a)

5

b)

6

c)

7

d)

8

106.

Point (3, 4) lies on the graph of the equation 3y = kx + 7. The value of k is:

a)

4/3

b)

5/3

c)

3

d)

7/3

107.

The graph of x = 3 is a line:

a)

Parallel to the x-axis at a distance of 3 units from the origin

b)

Parallel to the y-axis at a distance of 3 units from the origin

c)

Makes an intercept 3 on the x-axis

d)

Makes an intercept 3 on the y-axis

108.

What is the intersection of the x- axis and y-axis in the coordinate plane?

a)

origin

b)

ordinates

c)

coordinates axes

d)

abscissa

109.

Which of these points lie on Quadrant III?

a)

(6,-3)

b)

(5,10)

c)

(-2,-8)

d)

(-7,4)

110.

On which quadrant does (-1, 5) lie?

a)

I

b)

II

c)

III

d)

IV

111.

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?

a)

1/2

b)

−1/2

c)

2

d)

−2

112.

The pair of linear equations 3x + 5y = 3 ; 6x + ky = 8 do not have any solutions if :

a)

k = 5

b)

k = 10

c)

k ≠ 10

d)

k ≠ 5

113.

y=x-9

y=-4x

a)

x=7

y=1.8

b)

x=7.2

y=1.8

c)

x=1.8

y=-7.2

d)

x=1.88

y=7.2

114.

Solve and find the value of k for the following simultaneous equations:

3h − k = 2

2h + k = 8

a)

2

b)

4

c)

7

d)

10

115.

Solve for y
8x + 2y = -10

a)

y = -8x + 5

b)

y = -4x - 5

c)

y = -¹/₄ x - 10

d)

y = -¹/₄ x - 5

116.

Vertical or horizontal?
x = -3

a)

vertical

b)

horizontal

c)

neither

117.

Find the solution of the given simultaneous equations.

y\ =\ 2x-3

3x-2y=4

a)

(2, 1)

b)

$\left(-\frac{7}{3},-\frac{23}{3}\right)$

c)

(-7, -17)

d)

(7, 4)

e)

no solution

118.

Find the solution of the given simultaneous equation.
$3x+2y=3$
$5x+3y=4$

a)

(-1,3)

b)

(17, -12)

c)

$\left(\frac{1}{2},\frac{3}{4}\right)$

d)

(-6, 3)

119.

Solve simultaneously.

y=2x+1

y=-x-5

a)

(4, -9)

b)

(-2, -3)

c)

(7, 3)

d)

(-4, -7)

120.

If $4x=17$ is a linear equation in one variable, then $4x+0y=17$ is a linear equation in two variables.

a)

True

b)

False

c)

Can't say

d)

Its true as 17 is a prime number

121.

The line $y=kx$ is

a)

Passing through origin

b)

Passing through $\left(1,k\right)$

c)

Passing through $\left(k,k\right)$

d)

Passing through $\left(k,k^2\right)$

122.

The value of $k$ if $x=3\ ,\ y=2$ is a solution of the equation $5x+\frac{y}{2}=k$

a)

10

b)

12

c)

16

d)

18

123.

If $x=2\ and\ y=3$ are two lines in a cartesian plane, then

a)

Both the lines are parallel to x-axis.

b)

Both the lines are parallel to y-axis.

c)

$x=2$ is a line parallel to y-axis and $y=3$ is a line parallel to x-axis.

d)

both the lines coincide at $\left(2,3\right)$

124.

Which one of the following is/are a solution/s of the equation x+2y=6

a)

(2,2)

b)

(0,3)

c)

(6,0)

d)

(4,1)

125.

5x-4y + 8=0

7x+6y-9=0

This pair of linear equations is

a)

Consistent

b)

Inconsistent

126.

Intersecting lines

a)

No solution

b)

Unique solution

c)

Infinitely many solutions

d)

Two solutions

127.

5x - 3y = 11

-10 X + 6 Y = - 22

The pair of linear equations are

a)

Intersecting

b)

Parallel

c)

Concident

d)

None of them

128.

Purv what value of k the following pair of linear equations have infinitely many solutions

kx+ 3y- (k - 3) = 0

12 x + ky-k = 0

a)

K=6

b)

K≠3

c)

k=9

d)

k=3

linear equation in two variables class x

Total questions: 128

Worksheet time: 4hrs 53mins

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