https://file.aiquickdraw.com/mathbot/file/1726790874711nigk2pjq.jpg

We are given the system of equations:

\[
y = -5x + 7
\]
\[
2x - 2y = -2
\]

We will solve this system using substitution.

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

Since \( y = -5x + 7 \), substitute this into the second equation \( 2x - 2y = -2 \):

\[
2x - 2(-5x + 7) = -2
\]

### Step 2: Simplify the equation.

Distribute the \(-2\) across the expression \( -5x + 7 \):

\[
2x + 10x - 14 = -2
\]

Now combine like terms:

\[
12x - 14 = -2
\]

### Step 3: Solve for \( x \).

Add 14 to both sides of the equation:

\[
12x = 12
\]

Now divide both sides by 12:

\[
x = 1
\]

### Step 4: Substitute the value of \( x \) into the first equation to find \( y \).

Substitute \( x = 1 \) into the equation \( y = -5x + 7 \):

\[
y = -5(1) + 7 = -5 + 7 = 2
\]

### Final Solution:
The solution to the system of equations is:
\[
x = 1, \quad y = 2
\]

Would you like further details or have any questions?

### Related Questions:
1. How can you verify the solution to this system of equations?
2. What is the graphical interpretation of solving a system using substitution?
3. How does substitution compare to the elimination method in solving systems?
4. Can you solve the system using the elimination method and get the same result?
5. What happens if both equations describe the same line in the substitution method?

### Tip:
When substituting expressions in algebraic systems, always simplify carefully to avoid errors with distribution and combining terms.

Solve the system of equations: y = -5x + 7 and 2x - 2y = -2 using substitution.

Learn how to solve the system of linear equations y = -5x + 7 and 2x - 2y = -2 using the substitution method. This problem demonstrates algebraic techniques and is suitable for students in Grades 8-10.

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