https://r2.erweima.ai/mathbot/image/1726610197159za8u30et.jpg

Here are the equations from the image you've uploaded:

1. \( 8x + 2y = 18 \) (equation 4)
2. \( 4x + 1 = 9 + 4y \) (equation 6)
3. \( 3x - y = 12 \) (equation 8)
4. \( y + 5 = -(x - 3) \) (equation 10)
5. \( -y = 13 \) (equation 12)

Let's solve each one step by step:

### 1. Solve \( 8x + 2y = 18 \):
\[
8x + 2y = 18
\]
Divide through by 2:
\[
4x + y = 9
\]
So, the simplified equation is:
\[
y = 9 - 4x
\]

### 2. Solve \( 4x + 1 = 9 + 4y \):
\[
4x + 1 = 9 + 4y
\]
Subtract 9 from both sides:
\[
4x - 8 = 4y
\]
Divide by 4:
\[
x - 2 = y
\]
So the solution is:
\[
y = x - 2
\]

### 3. Solve \( 3x - y = 12 \):
\[
3x - y = 12
\]
Solve for \( y \):
\[
y = 3x - 12
\]

### 4. Solve \( y + 5 = -(x - 3) \):
\[
y + 5 = -(x - 3)
\]
Simplify the right-hand side:
\[
y + 5 = -x + 3
\]
Subtract 5 from both sides:
\[
y = -x - 2
\]

### 5. Solve \( -y = 13 \):
\[
-y = 13
\]
Multiply both sides by \(-1\):
\[
y = -13
\]

Let me know if you'd like any further clarifications or detailed steps.

Here are 5 relative questions to practice:
1. What is the slope of the line represented by the equation \( 4x + y = 9 \)?
2. How would you graph the equation \( y = 3x - 12 \)?
3. What happens to the value of \( y \) when \( x = 5 \) in the equation \( y = x - 2 \)?
4. Can you write the equation \( y = -x - 2 \) in standard form?
5. How does the equation \( -y = 13 \) represent a horizontal line on a graph?

**Tip:** When solving linear equations, always isolate one variable to simplify the equation and make graphing easier!

Solve the following equations:
1. 8x + 2y = 18
2. 4x + 1 = 9 + 4y
3. 3x - y = 12
4. y + 5 = -(x - 3)
5. -y = 13

Learn how to solve a system of linear equations with variables x and y. This step-by-step solution covers concepts such as simplifying equations and solving for variables. Ideal for students in Grades 7-9.

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