Question

solve this system of equations.
y = 3x - 6
y = -2x - 1
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 \( 3x - 6 \) equal to \( -2x - 1 \).
\( 3x - 6 = -2x - 1 \)

Step2: Solve for \( x \)

Add \( 2x \) to both sides:
\( 3x + 2x - 6 = -1 \)
\( 5x - 6 = -1 \)

Add 6 to both sides:
\( 5x = -1 + 6 \)
\( 5x = 5 \)

Divide both sides by 5:
\( x = \frac{5}{5} = 1 \)

Step3: Find \( y \)

Substitute \( x = 1 \) into one of the original equations, say \( y = 3x - 6 \):
\( y = 3(1) - 6 \)
\( y = 3 - 6 \)
\( y = -3 \)

Answer:

The solution to the system is \( x = 1 \), \( y = -3 \) (or the ordered pair \( (1, -3) \))