Question

1. find the solution of the system.

y = -2x - 7
2y - x = 1

Explanation:

Step1: Substitute \( y = -2x - 7 \) into \( 2y - x = 1 \)

Substitute \( y \) in the second equation: \( 2(-2x - 7) - x = 1 \)

Step2: Simplify the equation

Expand and combine like terms: \( -4x - 14 - x = 1 \) → \( -5x - 14 = 1 \)

Step3: Solve for \( x \)

Add 14 to both sides: \( -5x = 1 + 14 \) → \( -5x = 15 \)
Divide by -5: \( x = \frac{15}{-5} = -3 \)

Step4: Substitute \( x = -3 \) into \( y = -2x - 7 \)

Calculate \( y \): \( y = -2(-3) - 7 = 6 - 7 = -1 \)

Answer:

The solution is \( x = -3 \), \( y = -1 \) (or as an ordered pair \((-3, -1)\))