Question

Solve.

3x − 2y = –14
3x − 8y = –2

Answer 1

To solve the system of equations:

1. \(3x - 2y = -14\) (Equation 1)
2. \(3x - 8y = -2\) (Equation 2)

We can use the elimination method. First, let's subtract Equation 1 from Equation 2 to eliminate \(3x\).

\[
(3x - 8y) - (3x - 2y) = -2 - (-14)
\]

This simplifies to:

\[
-8y + 2y = -2 + 14
\]

\[
-6y = 12
\]

Now, divide both sides by -6:

\[
y = -2
\]

Now that we have the value of \(y\), we can substitute it back into Equation 1 to solve for \(x\):

\[
3x - 2(-2) = -14
\]

This simplifies to:

\[
3x + 4 = -14
\]

Now, subtract 4 from both sides:

\[
3x = -14 - 4
\]

\[
3x = -18
\]

Now, divide both sides by 3:

\[
x = -6
\]

Thus, the solution to the system of equations is:

\[
x = -6, \quad y = -2.
\]

So, the ordered pair \((-6, -2)\) is the solution.