Question

Use the substitution method to find the solutions to the system of equations.

y = 4x + 6

3x + 2y = 12

(1 point)
Responses

No solution
No solution

(0,6)
(0,6)

(6, 0)
(6, 0)

Infinite solutions
Infinite solutions
Question 7
17.

Answer 1

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:

1. \(y = 4x + 6\)
2. \(3x + 2y = 12\)

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)**