Given the system of equations.
{4x+y=8
{6x-9y=12
Which of the options represents the resulting equation after an equivalent expression for y is substituted into the second equation?
6 x - 9(-4 x + 8) = 12
6(4 x - 8) - 9 y = 12
4 x + 4 x - 8 = 8
6 x - 9(4 x - 8) = 12
The equivalent expression for y is y = 4x - 8 (found by solving the first equation for y). Substituting this into the second equation, we get:
6x - 9(4x - 8) = 12
Simplifying this equation gives us the resulting equation. Therefore, the answer is:
6x - 36x + 72 = 12
or
-30x = -60
x = 2
To find y, we can substitute this value of x into either of the original equations. Using the first equation:
4(2) + y = 8
y = 0
Therefore, the solution to the system of equations is (2, 0).