Question

solve the system by substitution.
y = 2x - 14
y = -5x

Explanation:

Step1: Substitute \( y = -5x \) into \( y = 2x - 14 \)

Since both equations are solved for \( y \), we can set them equal to each other. So we have \( -5x = 2x - 14 \).

Step2: Solve for \( x \)

Add \( 5x \) to both sides of the equation: \( 0 = 2x + 5x - 14 \), which simplifies to \( 0 = 7x - 14 \). Then add 14 to both sides: \( 14 = 7x \). Divide both sides by 7: \( x = \frac{14}{7} = 2 \).

Step3: Solve for \( y \)

Substitute \( x = 2 \) into \( y = -5x \). So \( y = -5(2) = -10 \).

Answer:

The solution to the system is \( x = 2 \) and \( y = -10 \), or the ordered pair \( (2, -10) \).