Which ordered pair is the solution to the system of equations?

Question

{y=3x−124x+6y=−6

Responses

(4, −7)
begin ordered pair 4 comma negative 7 end ordered pair

(6, −5)
begin ordered pair 6 comma negative 5 end ordered pair

(0, −12)
begin ordered pair 0 comma negative 12 end ordered pair

(3, −3)

Answer 1

To find the solution to the system of equations, we need to first rewrite the equations clearly.

The given system is:

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

We can substitute the expression for \(y\) from the first equation into the second equation.

Substituting \(y = 3x - 12\) into \(4x + 6y = -6\):

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

Now, simplify this:

\[ 4x + 18x - 72 = -6 \]

Combine like terms:

\[ 22x - 72 = -6 \]

Now, solve for \(x\):

\[ 22x = -6 + 72 \] \[ 22x = 66 \] \[ x = 3 \]

Now that we have \(x\), we can find \(y\) using the first equation:

\[ y = 3(3) - 12 \] \[ y = 9 - 12 \] \[ y = -3 \]

Thus, the solution to the system of equations is \( (3, -3) \).

From the provided responses, the solution is:

(3, −3)