Question

In the pair equations bx - 6y = 18 and 2x - 3y = 9, b is a constant. The system of two equations has infinitely many solutions. What is the value of b?
Show work or explain

Answer 1

Well, if

{bx - 6y = 18 and {2x - 3y = 9, you might want to try elimination

Multiply second equation by -2: bx - 6y = 18 and -2(2x - 3y = 9)

Simplified: bx - 6y = 18 and -4x + 6y = -18

Now if you add them you get: -4x + bx = 0

Then simplified:  bx = 4x

divide by x:  b = 4

Your final solution is b = 4.

Hope that helps!