Question

solve using elimination. 2x + 10y = -2 4x + 10y = -14 (□, □)

Explanation:

Step1: Subtract the first equation from the second equation to eliminate \( y \)

The two equations are:
\( 2x + 10y = -2 \) (Equation 1)
\( 4x + 10y = -14 \) (Equation 2)

Subtract Equation 1 from Equation 2:
\( (4x + 10y) - (2x + 10y) = -14 - (-2) \)
Simplify the left side: \( 4x + 10y - 2x - 10y = 2x \)
Simplify the right side: \( -14 + 2 = -12 \)
So we get \( 2x = -12 \)

Step2: Solve for \( x \)

Divide both sides of \( 2x = -12 \) by 2:
\( x = \frac{-12}{2} = -6 \)

Step3: Substitute \( x = -6 \) into Equation 1 to solve for \( y \)

Substitute \( x = -6 \) into \( 2x + 10y = -2 \):
\( 2(-6) + 10y = -2 \)
Simplify: \( -12 + 10y = -2 \)
Add 12 to both sides: \( 10y = -2 + 12 = 10 \)
Divide both sides by 10: \( y = \frac{10}{10} = 1 \)

Answer:

\((-6, 1)\)