Question

solve the system by substitution.

$-2y - 10 = x$

$-10x - y = -14$

Explanation:

Step1: Substitute \( x \) into the second equation

The first equation gives \( x = -2y - 10 \). Substitute this into the second equation \( -10x - y = -14 \). So we get \( -10(-2y - 10) - y = -14 \).

Step2: Simplify the equation

First, distribute the -10: \( 20y + 100 - y = -14 \). Then combine like terms: \( 19y + 100 = -14 \).

Step3: Solve for \( y \)

Subtract 100 from both sides: \( 19y = -14 - 100 = -114 \). Then divide by 19: \( y = \frac{-114}{19} = -6 \).

Step4: Solve for \( x \)

Substitute \( y = -6 \) into the first equation \( x = -2(-6) - 10 = 12 - 10 = 2 \).

Answer:

The solution to the system is \( x = 2 \), \( y = -6 \)