Question

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 for one variable and substitute it into the other equation. Let's solve Equation 2 for \( x \):

\[
x = 6y + 22
\]

Now, substitute \( x \) into Equation 1:

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

Distributing the 5:

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

Combine like terms:

\[
32y + 110 = 14
\]

Now, subtract 110 from both sides:

\[
32y = 14 - 110
\]
\[
32y = -96
\]

Now, divide by 32:

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

Now, substitute \( y = -3 \) back into the expression we derived for \( x \):

\[
x = 6(-3) + 22
\]
\[
x = -18 + 22
\]
\[
x = 4
\]

Thus, the solution to the system of equations is:

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