Question

Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items








Question
Solve the system of equations.
5x+2y=14

x−6y=22
(1 point)
(
,
)

Answer 1

To solve the system of equations:

1. \( 5x + 2y = 14 \) (Equation 1)
2. \( x - 6y = 22 \) (Equation 2)

We can solve it using substitution or elimination. Here, we will use substitution.

First, let’s solve Equation 2 for \( x \):

\[
x = 6y + 22
\]

Now we can substitute \( x \) in Equation 1:

\[
5(6y + 22) + 2y = 14
\]

Expanding this gives us:

\[
30y + 110 + 2y = 14
\]

Combine like terms:

\[
32y + 110 = 14
\]

Subtract 110 from both sides:

\[
32y = 14 - 110
\]

\[
32y = -96
\]

Now, divide by 32:

\[
y = \frac{-96}{32} = -3
\]

Now we know \( y \), we can substitute \( y \) back into the equation for \( x \):

\[
x = 6(-3) + 22
\]

\[
x = -18 + 22
\]

\[
x = 4
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (4, -3)
\]

So the final answer is:

\((4, -3)\)