Question

find real numbers a and b if
a(3x+1)+b(5x-1)=11x+9 for all x€r

Answer 1

you have

3ax + a + 5bx - b = 11x + 9

If these expressions are identical for all x, then like powers of x must be equal:

3a + 5b = 11
a - b = 9

so,

3(b+9) + 5b = 11
b = -2
a = 7