Question

solve the system by substitution.
\\(9y + 8 = x\\)
\\(-2x + 8y = -36\\)

Explanation:

Step1: Substitute \( x = 9y + 8 \) into the second equation

We have the second equation \( -2x + 8y = -36 \). Replace \( x \) with \( 9y + 8 \):
\( -2(9y + 8) + 8y = -36 \)

Step2: Simplify the left - hand side

First, distribute the - 2:
\( -18y-16 + 8y=-36 \)
Combine like terms:
\( (-18y + 8y)-16=-36 \)
\( -10y-16=-36 \)

Step3: Solve for \( y \)

Add 16 to both sides of the equation:
\( -10y-16 + 16=-36 + 16 \)
\( -10y=-20 \)
Divide both sides by - 10:
\( y=\frac{-20}{-10}=2 \)

Step4: Substitute \( y = 2 \) into the first equation to find \( x \)

The first equation is \( x = 9y+8 \). Substitute \( y = 2 \):
\( x=9\times2 + 8=18 + 8 = 26 \)

Answer:

The solution to the system is \( x = 26 \) and \( y = 2 \), or the ordered pair \( (26,2) \)