Question

Solve the following system of equations using the substitution method.

9x−3y=12

y+6=2x

(1 point)
Responses

There is no solution
There is no solution

There are infinite solutions
There are infinite solutions

(-2,-10)
(-2,-10)

(-10, -2)
(-10, -2)

Answer 1

To solve the system of equations using the substitution method, we first need to express one variable in terms of the other from one of the equations.

We have the following equations:

1) \( 9x - 3y = 12 \)
2) \( y + 6 = 2x \)

Let's solve the second equation for \( y \):

From equation 2:

\[
y + 6 = 2x
\]

Subtracting 6 from both sides gives:

\[
y = 2x - 6
\]

Now we will substitute \( y = 2x - 6 \) into the first equation:

Substituting into equation 1:

\[
9x - 3(2x - 6) = 12
\]

Distributing the -3:

\[
9x - 6x + 18 = 12
\]

Combine like terms:

\[
3x + 18 = 12
\]

Now, subtract 18 from both sides:

\[
3x = 12 - 18
\]
\[
3x = -6
\]

Dividing by 3:

\[
x = -2
\]

Now that we have \( x = -2 \), we can substitute it back into the equation we solved for \( y \):

\[
y = 2(-2) - 6
\]
\[
y = -4 - 6
\]
\[
y = -10
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-2, -10)
\]

So the correct answer is:

(-2, -10)