Question

from unit 4, lesson 13 solve the system of equations: \\(\

$$\begin{cases} y = 7x + 10 \\\\ y = -4x - 23 \\end{cases}$$

\\)

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 by 11: \( x = \frac{-33}{11} = -3 \)

Step3: Substitute \( x = -3 \) into one of the original equations to find \( y \)

Let's use \( y = 7x + 10 \). Substitute \( x = -3 \): \( y = 7(-3) + 10 \)
Simplify: \( y = -21 + 10 = -11 \)

Answer:

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