Question

solve this system of equations.
y = 7x + 10
y = -4x - 23
use the sketch tool or paper if it helps with your thinking.

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( 7x + 10 = -4x - 23 \)

Step2: Solve for \( x \)

Add \( 4x \) to both sides: \( 7x + 4x + 10 = -23 \)
Simplify: \( 11x + 10 = -23 \)
Subtract 10 from both sides: \( 11x = -23 - 10 \)
Simplify: \( 11x = -33 \)
Divide both sides by 11: \( x = \frac{-33}{11} = -3 \)

Step3: Solve for \( y \)

Substitute \( x = -3 \) into \( y = 7x + 10 \): \( y = 7(-3) + 10 \)
Simplify: \( y = -21 + 10 = -11 \)

Answer:

The solution to the system is \( x = -3 \), \( y = -11 \) (or the ordered pair \((-3, -11)\))