Question

solve the system by substitution. x = -y - 9; 6x - 5y = 1

Explanation:

Step1: Substitute \( x = -y - 9 \) into \( 6x - 5y = 1 \)

We replace \( x \) in the second equation with \( -y - 9 \). So we get \( 6(-y - 9) - 5y = 1 \).

Step2: Expand and simplify the equation

First, expand \( 6(-y - 9) \): \( -6y - 54 - 5y = 1 \). Then combine like terms: \( -11y - 54 = 1 \).

Step3: Solve for \( y \)

Add 54 to both sides: \( -11y = 1 + 54 \), which simplifies to \( -11y = 55 \). Then divide both sides by -11: \( y = \frac{55}{-11} = -5 \).

Step4: Substitute \( y = -5 \) back into \( x = -y - 9 \)

We get \( x = -(-5) - 9 = 5 - 9 = -4 \).

Answer:

The solution to the system is \( x = -4 \), \( y = -5 \)