Question

no additional details were added for this assignment. solve the system by substitution. x = 7y 3x - y = -40

Explanation:

Step1: Substitute \( x = 7y \) into \( 3x - y = -40 \)

We know \( x = 7y \), so replace \( x \) in the second equation with \( 7y \). The second equation \( 3x - y = -40 \) becomes \( 3(7y) - y = -40 \).

Step2: Simplify and solve for \( y \)

First, calculate \( 3(7y) = 21y \), so the equation is \( 21y - y = -40 \). Combine like terms: \( 20y = -40 \). Then divide both sides by 20: \( y = \frac{-40}{20} = -2 \).

Step3: Substitute \( y = -2 \) back into \( x = 7y \) to find \( x \)

Substitute \( y = -2 \) into \( x = 7y \), we get \( x = 7\times(-2) = -14 \).

Answer:

The solution to the system is \( x = -14 \), \( y = -2 \) (or as an ordered pair \( (-14, -2) \))