y=
2x−7
minus, 6, x, plus, 7, y, equals, 15
−6x+7y=
15

To solve the system of equations given:

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

we can use substitution or elimination. Let's use substitution since the first equation is already solved for \( y \).

### Step 1: Substitute \( y \) from the first equation into the second equation.

Given: 

\( y = 2x - 7 \)

Substituting \( y \) into the second equation:

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

### Step 2: Simplify and solve for \( x \).

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

\[
8x - 49 = 15
\]

Add 49 to both sides:

\[
8x = 64
\]

Divide by 8:

\[
x = 8
\]

### Step 3: Use the value of \( x \) to find \( y \).

Substituting \( x = 8 \) into the first equation:

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

\[
y = 16 - 7
\]

\[
y = 9
\]

### Solution

The solution to the system is:

\[
x = 8, \quad y = 9
\]

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. How do you use the elimination method to solve a system of equations?
2. What are the different methods to solve a system of linear equations?
3. How can we graphically represent the solution of a system of equations?
4. How do you check if a given point is a solution to a system of equations?
5. What are some applications of solving systems of linear equations in real life?

**Tip:** Always substitute the found values back into the original equations to verify your solution.

Learn how to solve a system of linear equations using substitution. This problem involves two equations: y = 2x - 7 and -6x + 7y = 15. Follow a detailed step-by-step solution and understand key algebraic concepts. Suitable for Grades 8-10.

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