y = 4x - 6 2x - 3y = 8 If this problem is to be solved by substitution, which is a correct step? Responses A 2x - 12x + 18 = 82x - 12x + 18 = 8 B 2x - 12x - 18 = 82x - 12x - 18 = 8 C 2x - 4x + 6 = 82x - 4x + 6 = 8 D 2x + 12x + 18 = 8
The correct step is option C: 2x - 4x + 6 = 8.
To solve the system of equations by substitution, we can start by isolating one variable in one of the equations and then substitute it into the other equation.
Given the equations:
y = 4x - 6
2x - 3y = 8
We can isolate y in the first equation:
y = 4x - 6
We can substitute this expression for y in the second equation:
2x - 3(4x - 6) = 8
Simplifying this equation gives us:
2x - 12x + 18 = 8
Which matches the step shown in option C.