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The image shows another system of linear equations. Let's solve it step by step.

### System 6:
\[
\begin{aligned}
2x + 5y &= -22 \quad \text{(Equation 1)} \\
4x - 3y &= 8 \quad \text{(Equation 2)}
\end{aligned}
\]

#### Step 1: Solve Equation 2 for \( y \).
First, solve Equation 2 for \( y \):

\[
4x - 3y = 8
\]
\[
-3y = -4x + 8
\]
\[
y = \frac{4x - 8}{3}
\]

#### Step 2: Substitute \( y = \frac{4x - 8}{3} \) into Equation 1.
\[
2x + 5\left(\frac{4x - 8}{3}\right) = -22
\]

To eliminate the fraction, multiply the entire equation by 3:
\[
3 \times 2x + 3 \times 5 \left(\frac{4x - 8}{3}\right) = 3 \times -22
\]
\[
6x + 20x - 40 = -66
\]
\[
26x - 40 = -66
\]

#### Step 3: Solve for \( x \).
\[
26x = -66 + 40
\]
\[
26x = -26
\]
\[
x = -1
\]

#### Step 4: Substitute \( x = -1 \) back into the expression for \( y \).
\[
y = \frac{4(-1) - 8}{3} = \frac{-4 - 8}{3} = \frac{-12}{3} = -4
\]

**Solution for System 6:**
\[
x = -1, \quad y = -4
\]

Would you like further explanation or have any questions about this solution?

Here are 5 related questions you might consider:
1. How would you solve this system using the substitution method?
2. What is the geometric meaning of the solution \( x = -1 \) and \( y = -4 \)?
3. Can you solve this system using the elimination method?
4. How can you verify the solution graphically?
5. What is the determinant of the coefficient matrix, and what does it tell you about the system?

**Tip:** When dealing with fractions in equations, multiplying through by the denominator early can simplify the solving process.

Learn how to solve a system of linear equations step-by-step using the substitution method. This problem involves solving the equations 2x + 5y = -22 and 4x - 3y = 8. Suitable for students in Grades 9-12.

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