Pair of Linear Equation inTwo Variables

The pair of equation x=2 and y=3 has

• A unique solution

• Two solutions

• Infinitely many solutions

• No solution

Write the value of k for which the system of equations x+y-4=0 and 2x+ky-3=0 has no solution

• k=2

• k=-3

• k=-7.5

• $k\ne2$

The sum of the digits of a two digit number is 12. If 18 is subtracted from it, the digits of the number get reversed. The number is

• 57

• 75

• 84

• 48

A pair of linear equations in two variables, which has a solution, is called a .......... pair of linear equations

• CONSISTENT

• INCONSISTENT

Find the value of k for which the equation kx+3y=(k-3) and 12x+ky=k have unique solution

• any number other than 6 and -6

• any number other than 3 and -3

• any natural number

• any real number

The pair of equations 4x-3y+5=0 and 8x-6y-10=0 graphically represents two lines which are

• Coincident

• Parallel

• Intersecting at exactly one point

• Intersecting at exactly two points

 $a_1x+b_1y+c_1=0\ ,\ a_2x+b_2y+c_2=0$  are a system of two simultaneous linear equations. If   $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$  , then the system has

• One solution
  

• Two solution
  

• Infinite solution
  

• NO solution
  

Find what value of k does the system of equations x+2y=3 and 5x+ky+7=0 have no solution.

• 10

• 12

• -10

• -11

If the system of equations 2x+3y=5 , 4x+ky=10 has infinitely many solutions, then k=

• 1

• 0.5

• 3

• 6

 $2x-3y-7$ 
 $\left(k+2\right)x-\left(2k+1\right)y=3\left(2k-1\right)$  

Find the value of k for which the above system of equations has infinitely many solutions

• No value
  

• -4

• Can not say
  

• 4