Question

determine the solution of the system of equations.\

$$\begin{cases}y = -6x + 4\\\\y = 2x + 12\\end{cases}$$

\
enter the correct answer in the boxes.

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( -6x + 4 = 2x + 12 \)

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( -6x - 2x + 4 = 12 \)
Simplify: \( -8x + 4 = 12 \)
Subtract 4 from both sides: \( -8x = 12 - 4 \)
Simplify: \( -8x = 8 \)
Divide both sides by -8: \( x = \frac{8}{-8} = -1 \)

Step3: Substitute \( x = -1 \) into one of the equations to find \( y \)

Let's use \( y = 2x + 12 \). Substitute \( x = -1 \): \( y = 2(-1) + 12 \)
Simplify: \( y = -2 + 12 = 10 \)

Answer:

\((-1, 10)\)