On solving 25 x + y − 3 x − y = 1 , \frac{25}{x+y}-\frac{3}{x-y}=1,\ \ x + y 2 5 − x − y 3 = 1 , and 40 x + y + 2 x − y = 5 \frac{40}{x+y}+\frac{2}{x-y}=5\ x + y 4 0 + x − y 2 = 5 , we get

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

x = 8 , y = 6 x=8,\ \ y=6 x = 8 , y = 6

x = 4 , y = 6 x=4,\ \ y=6 x = 4 , y = 6

What is the solution to a system of equations?

The point that the equations have in common.

The point where the two lines intersect.

There are several human beings and several dogs in a room. One tenth of the humans have lost a leg. The total numbers of feet are 77, then the number of dogs is

Not determinable due to insufficient data

The pair of equations a x + 2 y = 7 ax+2y=7 a x + 2 y = 7 a nd 3x+by=16 3 x + b y = 1 6 represent parallel lines if :

2 a − 3 b = 0 2a-3b=0 2 a − 3 b = 0

Solution of the system of equations 2 x − 5 y = 0 \sqrt{2}x-\sqrt{5}y=0 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x − 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> y = 0 and 5 x + 2 y = 0 \sqrt{5}x+\sqrt{2}y=0 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x + 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> y = 0 is

x = 0 , y = 0 x=0,\ \ y=0 x = 0 , y = 0

x = 5 , y = 2 x=\sqrt{5},\ \ y=\sqrt{2} x = 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , y = 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

x = − 2 , y = 5 x=-\sqrt{2},\ \ y=\sqrt{5} x = − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , y = 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

x = 2 , y = 5 x=\sqrt{2},\ \ y=\sqrt{5} x = 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , y = 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Class 10 th - Pair Of Linear Equations in Two Variables

Authored by Madan Kharbanda

Mathematics

10th Grade

CCSS covered

Used 1K+ times

Class 10 th - Pair Of Linear Equations in Two Variables

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15 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$x=8,\ \ y=6$

$x=4,\ \ y=6$

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

None of these

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

$m=1$

$m=2$

$m=-1$

$m=-2$

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

In a bag containing red and white balls, half the number of white balls is equal to one-third the number of red balls. Thrice the total number of balls exceeds seven times the number of white balls by 6. How many balls of each colour does the bag contain ?

Red balls = 12 , and White balls = 10

Red balls = 10 , and White balls = 10

Red balls = 8 , and White balls = 12

Red balls = 18 , and White balls = 12

Tags

CCSS.8.EE.C.8C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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.

$x=2,\ \ y=3$

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

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

None of these

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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

only one solution

no solution

only two solution

infinite solution

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The sum of a two digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number. Find the first number.

Tags

CCSS.8.EE.C.7B

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

$k=-4$

$k=6$

$k=-3$

$k=2$

Tags

CCSS.8.EE.C.8B

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Class 10 th - Pair Of Linear Equations in Two Variables

On solving 25x+y−3x−y=1, \frac{25}{x+y}-\frac{3}{x-y}=1,\ \ x+y25​−x−y3​=1, and 40x+y+2x−y=5 \frac{40}{x+y}+\frac{2}{x-y}=5\ x+y40​+x−y2​=5 , we get

Solve 2x+3y=112x+3y=112x+3y=11 and 2x−4y=−242x-4y=-242x−4y=−24 and hence find the value of 'm' for which y=mx+3y=mx+3

In a bag containing red and white balls, half the number of white balls is equal to one-third the number of red balls. Thrice the total number of balls exceeds seven times the number of white balls by 6. How many balls of each colour does the bag contain ?

The path of a train A is given by the equation x+2y−4=0x+2y-4=0x+2y−4=0 and the path of another train B is given by the equation 2x+4y−12=02x+4y-12=02x+4y−12=0 . Will the paths cross ? Solve by the method of substitution.

The equations 2x−3y+5=02x-3y+5=02x−3y+5=0 and 6y−4x=106y-4x=106y−4x=10 , when solved simultaneously, have :

The sum of a two digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number. Find the first number.

For what values of k will the following pair of linear equations have infinitely many solutions ? kx+3y−(k−3)=0kx+3y-\left(k-3\right)=0kx+3y−(k−3)=0 and 12x+ky−k=012x+ky-k=012x+ky−k=0

What is the solution to a system of equations?

There are several human beings and several dogs in a room. One tenth of the humans have lost a leg. The total numbers of feet are 77, then the number of dogs is

Ganesh has to pay Rs. 482 for 19 apples and 11 guavas. If he would have exchanged the number of apples and guavas purchased, then he would have paid Rs.64 less. Find how much more amount he has to pay to purchase 1 apple than 1 guava

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

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

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.

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

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