Question

solve the following system of equations. -5x + 2y = 6 10x - 2y = -16 x = \boxed{} y = \boxed{}

Explanation:

Step1: Label the equations

Let the first equation be \( -5x + 2y = 6 \) (Equation 1) and the second be \( 10x - 2y = -16 \) (Equation 2).

Step2: Add the two equations

Adding Equation 1 and Equation 2 to eliminate \( y \):
\[

$$\begin{align*} (-5x + 2y) + (10x - 2y) &= 6 + (-16)\\ -5x + 10x + 2y - 2y &= 6 - 16\\ 5x &= -10 \end{align*}$$

\]

Step3: Solve for \( x \)

Divide both sides of \( 5x = -10 \) by 5:
\[
x = \frac{-10}{5} = -2
\]

Step4: Substitute \( x = -2 \) into Equation 1

Substitute \( x = -2 \) into \( -5x + 2y = 6 \):
\[
-5(-2) + 2y = 6\\
10 + 2y = 6
\]

Step5: Solve for \( y \)

Subtract 10 from both sides:
\[
2y = 6 - 10\\
2y = -4
\]
Divide both sides by 2:
\[
y = \frac{-4}{2} = -2
\]

Answer:

\( x = -2 \), \( y = -2 \)