https://file.aiquickdraw.com/mathbot/file/17254037899512x10nit1.jpg

The system of equations given in the image is:

\[
\begin{aligned}
1) & \quad 3x - 6y = 24 \\
2) & \quad 4x + 5y = -7
\end{aligned}
\]

To solve this system, we'll use either the substitution method or the elimination method. I'll use the elimination method here.

### Step 1: Multiply the equations to align coefficients for elimination
To eliminate \(x\), we can multiply the first equation by 4 and the second equation by 3:

\[
\begin{aligned}
(1) \times 4 & : \quad 12x - 24y = 96 \\
(2) \times 3 & : \quad 12x + 15y = -21
\end{aligned}
\]

### Step 2: Subtract the equations
Now, subtract the second equation from the first to eliminate \(x\):

\[
(12x - 24y) - (12x + 15y) = 96 - (-21)
\]

Simplifying, we get:

\[
-39y = 117
\]

### Step 3: Solve for \(y\)
Divide both sides by -39:

\[
y = \frac{117}{-39} = -3
\]

### Step 4: Substitute \(y = -3\) back into one of the original equations
Substitute \(y = -3\) into the first equation \(3x - 6y = 24\):

\[
3x - 6(-3) = 24
\]

Simplifying:

\[
3x + 18 = 24
\]

Subtract 18 from both sides:

\[
3x = 6
\]

Divide by 3:

\[
x = 2
\]

### Solution
The solution to the system of equations is:

\[
x = 2, \quad y = -3
\]

Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. How can we verify the solution to a system of linear equations?
2. What is the difference between the substitution method and the elimination method?
3. How can graphing be used to solve a system of equations?
4. How do you solve a system of equations that has no solution or infinite solutions?
5. How can systems of equations be applied to real-world problems?

**Tip:** Always double-check your solution by substituting the values of \(x\) and \(y\) back into the original equations. This ensures that the solution satisfies both equations.

Solve the system of equations below: 3x - 6y = 24 and 4x + 5y = -7.

Learn how to solve the system of linear equations 3x - 6y = 24 and 4x + 5y = -7 using the elimination method. This problem demonstrates key algebraic concepts and is suitable for students in Grades 9-12.

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