https://file.aiquickdraw.com/mathbot/file/17283985588868rqcouyl.jpg

I'll solve the systems of equations from the image you provided. Each system will be solved using substitution as the instruction suggests.

### Problem 1:
\[
4x - 11y = 18 \quad \text{(1)} \\
x + 3y = -7 \quad \text{(2)}
\]
Solve equation (2) for \(x\):
\[
x = -3y - 7
\]
Substitute into equation (1):
\[
4(-3y - 7) - 11y = 18 \\
-12y - 28 - 11y = 18 \\
-23y = 46 \\
y = -2
\]
Substitute \(y = -2\) into \(x = -3y - 7\):
\[
x = -3(-2) - 7 = 6 - 7 = -1
\]
Solution: \(x = -1\), \(y = -2\)

### Problem 2:
\[
-3x - 2y = -16 \quad \text{(1)} \\
x - 2y = -24 \quad \text{(2)}
\]
Solve equation (2) for \(x\):
\[
x = 2y - 24
\]
Substitute into equation (1):
\[
-3(2y - 24) - 2y = -16 \\
-6y + 72 - 2y = -16 \\
-8y = -88 \\
y = 11
\]
Substitute \(y = 11\) into \(x = 2y - 24\):
\[
x = 2(11) - 24 = 22 - 24 = -2
\]
Solution: \(x = -2\), \(y = 11\)

### Problem 3:
\[
-2x + y = -8 \quad \text{(1)} \\
-3x - 11y = 13 \quad \text{(2)}
\]
Solve equation (1) for \(y\):
\[
y = 2x - 8
\]
Substitute into equation (2):
\[
-3x - 11(2x - 8) = 13 \\
-3x - 22x + 88 = 13 \\
-25x = -75 \\
x = 3
\]
Substitute \(x = 3\) into \(y = 2x - 8\):
\[
y = 2(3) - 8 = 6 - 8 = -2
\]
Solution: \(x = 3\), \(y = -2\)

### Problem 4:
\[
-6x + y = 0 \quad \text{(1)} \\
-5x - 5y = -35 \quad \text{(2)}
\]
Solve equation (1) for \(y\):
\[
y = 6x
\]
Substitute into equation (2):
\[
-5x - 5(6x) = -35 \\
-5x - 30x = -35 \\
-35x = -35 \\
x = 1
\]
Substitute \(x = 1\) into \(y = 6x\):
\[
y = 6(1) = 6
\]
Solution: \(x = 1\), \(y = 6\)

### Problem 5:
\[
-2x + 3y = -3 \quad \text{(1)} \\
x - 2y = 6 \quad \text{(2)}
\]
Solve equation (2) for \(x\):
\[
x = 2y + 6
\]
Substitute into equation (1):
\[
-2(2y + 6) + 3y = -3 \\
-4y - 12 + 3y = -3 \\
-y = 9 \\
y = -9
\]
Substitute \(y = -9\) into \(x = 2y + 6\):
\[
x = 2(-9) + 6 = -18 + 6 = -12
\]
Solution: \(x = -12\), \(y = -9\)

### Problem 6:
\[
10x + 10y = -10 \quad \text{(1)} \\
x - 7y = -1 \quad \text{(2)}
\]
Simplify equation (1):
\[
x + y = -1
\]
Solve equation (1) for \(x\):
\[
x = -1 - y
\]
Substitute into equation (2):
\[
(-1 - y) - 7y = -1 \\
-1 - 8y = -1 \\
-8y = 0 \\
y = 0
\]
Substitute \(y = 0\) into \(x = -1 - y\):
\[
x = -1 - 0 = -1
\]
Solution: \(x = -1\), \(y = 0\)

### Problem 7:
\[
-5x + 6y = -32 \quad \text{(1)} \\
x - 11y = -23 \quad \text{(2)}
\]
Solve equation (2) for \(x\):
\[
x = 11y - 23
\]
Substitute into equation (1):


I need all the solutions to the systems of equations in the image provided.

This page offers step-by-step solutions to systems of linear equations using the substitution method. Each solution involves solving for one variable and substituting it into the second equation. Suitable for students in Grades 9-12 studying Algebra.

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