Question

Solve the system by substitution.
9, y, plus, 8, equals, x
9y+8=
x
minus, 2, x, plus, 8, y, equals, minus, 36
−2x+8y=
−36
Answer
Attempt 1 out of 2

left parenthesis(
,
right parenthesis) Submit Answer

Answer 1

To solve the system of equations using substitution, we have:

1. \( x = 9y + 8 \)
2. \( -2x + 8y = -36 \)

First, we can substitute the expression for \( x \) from the first equation into the second equation.

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

\[
-2(9y + 8) + 8y = -36
\]

Now, distribute \(-2\):

\[
-18y - 16 + 8y = -36
\]

Combine like terms:

\[
-18y + 8y - 16 = -36
\]
\[
-10y - 16 = -36
\]

Next, add 16 to both sides:

\[
-10y = -20
\]

Now, divide by -10:

\[
y = 2
\]

Now, we can substitute \( y = 2 \) back into the first equation to find \( x \):

\[
x = 9(2) + 8
\]
\[
x = 18 + 8
\]
\[
x = 26
\]

Now we have the solution:

\[
(x, y) = (26, 2)
\]

So the solution to the system of equations is:

\[
\boxed{(26, 2)}
\]