Question

resolver el sistema por eliminación.
solve the system with the elimination method:
\

$$\begin{cases}8x + y = -2\\\\-2x + 2y = 14\\end{cases}$$

answer: $(x, y) = (\square, \square)$
enter your answers as integers or as reduced fraction(s) in the form a/b.
question help: \video

Explanation:

Step1: Multiply first equation

To eliminate \( y \), multiply the first equation \( 8x + y = -2 \) by \( 2 \). We get \( 16x + 2y = -4 \).

Step2: Subtract second equation

Subtract the second equation \( -2x + 2y = 14 \) from the new first equation \( 16x + 2y = -4 \). So, \((16x + 2y) - (-2x + 2y) = -4 - 14\). Simplifying gives \( 18x = -18 \).

Step3: Solve for x

Divide both sides of \( 18x = -18 \) by \( 18 \). We have \( x = \frac{-18}{18} = -1 \).

Step4: Substitute x into first equation

Substitute \( x = -1 \) into \( 8x + y = -2 \). So, \( 8(-1) + y = -2 \), which simplifies to \( -8 + y = -2 \).

Step5: Solve for y

Add \( 8 \) to both sides: \( y = -2 + 8 = 6 \).

Answer:

\((-1, 6)\)