Question

solve the system by substitution.
$6x - 2y = 26$
$-y + 3 = x$

Explanation:

Step1: Substitute \( x = -y + 3 \) into \( 6x - 2y = 26 \)

We know from the second equation that \( x = -y + 3 \). Substitute this expression for \( x \) into the first equation \( 6x - 2y = 26 \). So we get \( 6(-y + 3) - 2y = 26 \).

Step2: Simplify the equation

First, distribute the 6 in \( 6(-y + 3) \): \( -6y + 18 - 2y = 26 \). Then combine like terms: \( -8y + 18 = 26 \). Subtract 18 from both sides: \( -8y = 26 - 18 \), which simplifies to \( -8y = 8 \). Divide both sides by -8: \( y = \frac{8}{-8} = -1 \).

Step3: Find the value of \( x \)

Now substitute \( y = -1 \) into the equation \( x = -y + 3 \). So \( x = -(-1) + 3 = 1 + 3 = 4 \).

Answer:

The solution to the system is \( x = 4 \), \( y = -1 \)