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 1

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

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

Since Equation 1 is already solved for \( y \), we can substitute \( y \) in Equation 2.

### Substitute \( y \) in Equation 2:

Substituting \( y \) from Equation 1 into Equation 2:

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

### Distribute and simplify:

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

Combine like terms:

\[
8x - 49 = 15
\]

### Solve for \( x \):

Add 49 to both sides:

\[
8x = 15 + 49
\]
\[
8x = 64
\]

Now, divide by 8:

\[
x = 8
\]

### Find \( y \):

Now substitute \( x = 8 \) back into Equation 1 to find \( y \):

\[
y = 2(8) - 7
\]
\[
y = 16 - 7
\]
\[
y = 9
\]

### Solution:

The solution to the system of equations is:

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

### Verification:

To ensure the solution is correct, we can substitute \( x \) and \( y \) back into both original equations.

1. For the first equation:
\[
y = 2x - 7 \implies 9 = 2(8) - 7 \implies 9 = 16 - 7 \implies 9 = 9 \quad \text{(True)}
\]

2. For the second equation:
\[
-6x + 7y = 15 \implies -6(8) + 7(9) = 15 \implies -48 + 63 = 15 \implies 15 = 15 \quad \text{(True)}
\]

Both equations are satisfied, confirming that the solution \( (8, 9) \) is correct.