Question

If the system of equations 2x+3y=7 and (a+b)x + (2a-b)y=21 has infinitely many solutions,then find the values of a and b

Answer 1

Consider the first equation.

2x + 3y = 7.

I liked to multiply 3 to both the sides.

6x + 9y = 21.

Now take the second equation.

(a+b)x + (2a-b)y = 21

Well, the RHS of both is same now, 21. So we can say,

a + b = 6     →     (1)

2a - b = 9      →      (2)

Add (1) and (2). We get,

3a = 15     ⇒     a = 5

So,   b = 1