Complete this assessment to review what you've learned. It will not count toward your grade.

Question

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:

\((4, -3)\)