Question

if the system of the equation 2x+3y=7 and (a+b)x+(2a-b)y=21 has infinite. number of solutions then the value of a and b​

Answer 1

First equation  2x+3y=7

Second equation  (a+b)x+(2a-b)y=21

These two linear equations in two variables can be solved easily by elimination method.

Firstly, multiply the first equation by 2 that gives 10x + 2y = 10   ----- (i)

Now subtract (i) from second equation, that gives

10x – 10x + 3y – 2y = 20 – 10

=>  a = 10

Putting value of y in first equation,

5x + 10 = 5

5x = -5

=>  b = -1.