Question

solve the system by substitution.
$9y - 6 = x$
$2x - 8y = 18$

Explanation:

Step1: Substitute \( x = 9y - 6 \) into the second equation

We have the second equation \( 2x - 8y = 18 \). Replace \( x \) with \( 9y - 6 \), so we get \( 2(9y - 6) - 8y = 18 \).

Step2: Simplify and solve for \( y \)

First, expand the left - hand side: \( 18y-12 - 8y=18 \). Combine like terms: \( 10y-12 = 18 \). Add 12 to both sides: \( 10y=18 + 12=30 \). Then divide both sides by 10: \( y=\frac{30}{10}=3 \).

Step3: Substitute \( y = 3 \) into the first equation to find \( x \)

The first equation is \( x = 9y-6 \). Substitute \( y = 3 \) into it: \( x=9\times3 - 6=27 - 6 = 21 \).

Answer:

The solution to the system of equations is \( x = 21 \) and \( y = 3 \) (or the ordered pair \((21,3)\)).