Question

Find the value of a and b .
2x+3y=7 and 2ax+ay=28-by

Answer 1

Given system of equations is:

2x + 3y = 7 and

2ax + ay = 28 - by

The above equations can be rewritten as:

2x + 3y - 7 = 0 and

2ax + (a + b)y - 28 = 0

Here the system must have infinite solutions. We know that, for the given system of equations to have infinitely many solutions,

a1/a2 = b1/b2 = c1/c2
i.e
2/2a = 3/(a+b) = -7/-28
1/a = 3/(a+b) = 1/4

1/a = 1/4
a = 4

3/(a+b) = 1/4
a+b = 12
4+b = 12
b = 8