https://file.aiquickdraw.com/mathbot/file/1730121803914h4pzgex2.jpg

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

\[
x = -y + 2
\]
\[
4x - 6y = -22
\]

### Step 1: Substitute \( x \) from the first equation into the second equation
Since \( x = -y + 2 \), we can replace \( x \) in the second equation:

\[
4(-y + 2) - 6y = -22
\]

Expanding this, we get:

\[
-4y + 8 - 6y = -22
\]

Combine like terms:

\[
-10y + 8 = -22
\]

### Step 2: Solve for \( y \)
Subtract 8 from both sides:

\[
-10y = -30
\]

Then, divide by \(-10\):

\[
y = 3
\]

### Step 3: Substitute \( y = 3 \) back into the first equation to find \( x \)
Using \( x = -y + 2 \):

\[
x = -(3) + 2 = -3 + 2 = -1
\]

### Solution
The solution to the system is:

\[
(x, y) = (-1, 3)
\]

Would you like more details or have any questions?

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Here are some related questions to practice:

1. How would you solve a system of equations if both equations were already solved for \( x \)?
2. What is the graphical interpretation of the solution to this system of equations?
3. How do you check if a solution is correct for a given system of equations?
4. Can you solve this system using the elimination method instead of substitution?
5. How would the solution change if the second equation were \( 4x - 6y = -20 \) instead?

**Tip:** When using substitution, always double-check your substituted values to avoid errors in simplification!

Solve the system by substitution:

x = -y + 2
4x - 6y = -22

Step-by-step solution for solving a system of linear equations using substitution. In this example, we solve x = -y + 2 and 4x - 6y = -22 by substituting one equation into the other and simplifying. Suitable for Grades 8-10 students learning algebra and systems of equations.

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