Question

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

x−6y=22

Answer 1

To solve the system of equations

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

we can use the substitution or elimination method. Here, I'll use the substitution method.

First, we can solve Equation 2 for \( x \):

\[
x = 6y + 22
\]

Now, we'll substitute this expression for \( x \) in Equation 1:

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

Expanding this:

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

Combining the \( y \) terms:

\[
32y + 110 = 14
\]

Next, we will isolate \( y \) by subtracting 110 from both sides:

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

Now, we divide by 32:

\[
y = -3
\]

Now that we have \( y \), we can substitute it back into the equation we found for \( x \):

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

Thus, the solution to the system of equations is:

\[
x = 4, \quad y = -3
\]

So the solution is \( (4, -3) \).