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

Answer 1

To solve the system of equations using the substitution method, we start with the given equations:

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

We will substitute \( y \) from the first equation into the second equation.

Substituting \( y \) into the second equation:

\[
3x + 2(4x + 6) = 12
\]

Now, simplify the equation:

\[
3x + 8x + 12 = 12
\]

Combine like terms:

\[
11x + 12 = 12
\]

Subtract 12 from both sides:

\[
11x = 0
\]

Now, solve for \( x \):

\[
x = 0
\]

Now that we have \( x \), we can find \( y \) by substituting \( x = 0 \) back into the first equation:

\[
y = 4(0) + 6 = 6
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (0, 6)
\]

Therefore, the answer is:

**(0, 6)**