Question

Solve the system by substitution.
y, equals, 2, x, minus, 7
y=
2x−7
minus, 6, x, plus, 7, y, equals, 15
−6x+7y=
15
Answer
Attempt 1 out of 2

left parenthesis(
,
right parenthesis) Submit Answer

Answer 1

To solve the given system of equations by substitution, we start with the two equations:

1. \( y = 2x - 7 \) (Equation 1)
2. \( -6x + 7y = 15 \) (Equation 2)

We will substitute Equation 1 into Equation 2.

Substituting \( y = 2x - 7 \) into Equation 2:

\[
-6x + 7(2x - 7) = 15
\]

Now, expand the left side:

\[
-6x + 14x - 49 = 15
\]

Combine like terms:

\[
8x - 49 = 15
\]

Next, add 49 to both sides:

\[
8x = 15 + 49
\]

\[
8x = 64
\]

Now, divide both sides by 8 to solve for \( x \):

\[
x = 8
\]

Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):

\[
y = 2(8) - 7
\]

\[
y = 16 - 7
\]

\[
y = 9
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (8, 9)
\]

**Final Answer:**

\((8, 9)\)