Solve the system of equations by graphing.
3x
minus2y
equalsnegative 24
negative 3x
minus y
equals6
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Part 1
Use the graphing tool to graph the system.

Part 2
Determine the solution set. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set is StartSet nothing EndSet
  
.
​(Type an ordered​ pair.)
B.
There are infinitely many solutions.
C.
The solution set is the empty set.

Let's solve this system of equations step-by-step, starting with rewriting both equations in slope-intercept form \( y = mx + b \) to make graphing easier.

### Step 1: Rewrite the equations.

1. The first equation is:
   \[
   3x - 2y = -24
   \]
   Solve for \( y \):
   \[
   -2y = -3x - 24
   \]
   Divide both sides by \( -2 \):
   \[
   y = \frac{3}{2}x + 12
   \]

2. The second equation is:
   \[
   -3x - y = 6
   \]
   Solve for \( y \):
   \[
   -y = 3x + 6
   \]
   Divide both sides by \( -1 \):
   \[
   y = -3x - 6
   \]

### Step 2: Graph both equations.

- The first equation, \( y = \frac{3}{2}x + 12 \), has a slope of \( \frac{3}{2} \) and a y-intercept of \( 12 \).
- The second equation, \( y = -3x - 6 \), has a slope of \( -3 \) and a y-intercept of \( -6 \).

When we graph these two lines, we find that they intersect at a single point. Let's calculate the solution algebraically for confirmation.

### Step 3: Solve algebraically.

We will use substitution or elimination to solve for the intersection point. Since both equations are already solved for \( y \), set them equal to each other:
\[
\frac{3}{2}x + 12 = -3x - 6
\]
Multiply everything by 2 to eliminate the fraction:
\[
3x + 24 = -6x - 12
\]
Now, solve for \( x \):
\[
3x + 6x = -12 - 24
\]
\[
9x = -36
\]
\[
x = -4
\]

Now substitute \( x = -4 \) into one of the original equations to solve for \( y \). Using \( y = -3x - 6 \):
\[
y = -3(-4) - 6 = 12 - 6 = 6
\]

Thus, the solution is \( (-4, 6) \).

### Step 4: Determine the solution set.

The system of equations has a single solution: \( (-4, 6) \).

The correct answer is:
\[
\boxed{A. \text{The solution set is } (-4, 6)}
\]

---

Would you like more details on any step? Here are five related questions for further practice:

1. How do you graph a line using the slope and y-intercept?
2. What are the different methods to solve a system of linear equations?
3. How can you check if a point is a solution to a system of equations?
4. What does it mean if two lines have the same slope but different y-intercepts?
5. How do you solve a system of equations using substitution?

**Tip:** Always double-check your graph for accuracy when solving systems of equations by graphing!

Solve the system of equations by graphing. 3x - 2y = -24, -3x - y = 6. Determine the solution set. A. The solution set is an ordered pair. B. There are infinitely many solutions. C. The solution set is the empty set.

Learn how to solve the system of linear equations 3x - 2y = -24 and -3x - y = 6 by graphing. This step-by-step guide covers the slope-intercept form, graphing techniques, and solving the system algebraically to determine the solution. Suitable for Grades 8-10.

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