olve the system by graphing.

 5x + y = -16
 2x + 5y = 12

To solve the system of equations by graphing, we will follow these steps:

### Given System:
1. \( 5x + y = -16 \)
2. \( 2x + 5y = 12 \)

### Step 1: Rewrite each equation in slope-intercept form (\(y = mx + b\)).

#### First Equation: \( 5x + y = -16 \)
Solve for \(y\):
\[
y = -5x - 16
\]
This is in slope-intercept form where the slope \(m = -5\) and the y-intercept is \(-16\).

#### Second Equation: \( 2x + 5y = 12 \)
Solve for \(y\):
\[
5y = -2x + 12
\]
\[
y = -\frac{2}{5}x + \frac{12}{5}
\]
This is also in slope-intercept form where the slope \(m = -\frac{2}{5}\) and the y-intercept is \(\frac{12}{5}\).

### Step 2: Plot the equations.

- For the first equation \(y = -5x - 16\):
  - Start at the y-intercept of \(-16\) and use the slope \( -5 \), which means go down 5 units and right 1 unit to plot more points.

- For the second equation \(y = -\frac{2}{5}x + \frac{12}{5}\):
  - Start at the y-intercept of \( \frac{12}{5} \approx 2.4 \) and use the slope \( -\frac{2}{5} \), which means go down 2 units and right 5 units to plot additional points.

### Step 3: Find the intersection point.
The solution of the system will be the point where these two lines intersect.

Since I can't draw the graph, you can plot it manually using the information above. Alternatively, I can calculate the solution algebraically if you prefer.

Would you like more details on this, or should I proceed with solving it algebraically?

### Five related questions:
1. How do you graph a linear equation using its slope and intercept?
2. What is the significance of the intersection point in a system of linear equations?
3. How do we determine the number of solutions a system of equations might have by graphing?
4. Can systems of equations have no solution or infinitely many solutions? How does this appear on a graph?
5. How would changing the coefficients in the given equations affect the graph?

### Tip:
When graphing equations, always check your plotted points carefully to ensure accuracy in finding the intersection point.

Solve the system by graphing.
5x + y = -16
2x + 5y = 12

Learn how to solve a system of linear equations by graphing the equations 5x + y = -16 and 2x + 5y = 12. This problem covers key algebraic concepts, including converting equations to slope-intercept form and finding the intersection point. Suitable for students in Grades 8-10.

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