For what numbers a and b is the system of equations below sa

For what numbers a and b is the system of equations below satisfied by x=b and y=a?

x-5y=a

6x+2y=190

Solution

Setting ,x=b and y=a in first equation gives

b-5a=a

b=6a

Setting , x=b,y=a in second equation gives

6b+2a=190

But, b=6a

Substituting gives

36a+2a=190

38a=190

a=5

Hence, b=30