To solve the system of equations using the substitution method, we will substitute the expression for \(y\) from the first equation into the second equation.
We have the system:
- \(y = 4x + 6\)
- \(3x + 2y = 12\)
Now, substitute equation (1) into equation (2):
\[ 3x + 2(4x + 6) = 12 \]
Now, simplify and solve for \(x\):
\[ 3x + 8x + 12 = 12 \] \[ 11x + 12 = 12 \] \[ 11x = 12 - 12 \] \[ 11x = 0 \] \[ x = 0 \]
Now that we have \(x = 0\), substitute back into the first equation to find \(y\):
\[ y = 4(0) + 6 = 6 \]
Thus, the solution to the system of equations is:
\[ (0, 6) \]
So, the correct response is:
(0, 6)
1 answer