Question

solve using substitution.
8x + 9y = 9
x + 2y = 9
(\boxed{\quad}, \boxed{\quad})

Explanation:

Step1: Solve the second equation for x

From \( x + 2y = 9 \), we can express \( x \) as \( x = 9 - 2y \).

Step2: Substitute x into the first equation

Substitute \( x = 9 - 2y \) into \( 8x + 9y = 9 \):
\[

$$\begin{align*} 8(9 - 2y) + 9y &= 9\\ 72 - 16y + 9y &= 9\\ 72 - 7y &= 9 \end{align*}$$

\]

Step3: Solve for y

Subtract 72 from both sides:
\[
-7y = 9 - 72 = -63
\]
Divide both sides by -7:
\[
y = \frac{-63}{-7} = 9
\]

Step4: Substitute y back to find x

Substitute \( y = 9 \) into \( x = 9 - 2y \):
\[
x = 9 - 2(9) = 9 - 18 = -9
\]

Answer:

\((-9, 9)\)