Question

Solve the following system of equations graphically on the set of axes below.
y= -1/5x - 8
y= 3/5x - 4
what is the solution and the points to plot down on the plot?

Answer 1

To solve the system of equations graphically, we will first identify points to plot for each equation. Here are the equations you provided:

1. \( y = -\frac{1}{5}x - 8 \)
2. \( y = \frac{3}{5}x - 4 \)

### Step 1: Choose Values for \(x\) and Calculate \(y\)

**For the first equation** \( y = -\frac{1}{5}x - 8 \):

- **When \( x = 0 \)**:
\[
y = -\frac{1}{5}(0) - 8 = -8 \quad \Rightarrow \quad (0, -8)
\]

- **When \( x = 5 \)**:
\[
y = -\frac{1}{5}(5) - 8 = -1 - 8 = -9 \quad \Rightarrow \quad (5, -9)
\]

- **When \( x = -5 \)**:
\[
y = -\frac{1}{5}(-5) - 8 = 1 - 8 = -7 \quad \Rightarrow \quad (-5, -7)
\]

**Points to plot for the first equation**:
- (0, -8)
- (5, -9)
- (-5, -7)

**For the second equation** \( y = \frac{3}{5}x - 4 \):

- **When \( x = 0 \)**:
\[
y = \frac{3}{5}(0) - 4 = -4 \quad \Rightarrow \quad (0, -4)
\]

- **When \( x = 5 \)**:
\[
y = \frac{3}{5}(5) - 4 = 3 - 4 = -1 \quad \Rightarrow \quad (5, -1)
\]

- **When \( x = -5 \)**:
\[
y = \frac{3}{5}(-5) - 4 = -3 - 4 = -7 \quad \Rightarrow \quad (-5, -7)
\]

**Points to plot for the second equation**:
- (0, -4)
- (5, -1)
- (-5, -7)

### Step 2: Plotting the Points

You can plot the points on a graph:

**For the first equation** \( y = -\frac{1}{5}x - 8 \):
- (0, -8)
- (5, -9)
- (-5, -7)

**For the second equation** \( y = \frac{3}{5}x - 4 \):
- (0, -4)
- (5, -1)
- (-5, -7)

### Step 3: Draw the Lines

Draw a straight line through the points of each equation on the graph.

### Step 4: Find the Intersection

The solution is the point where the two lines intersect.

Looking at the points plotted, the intersection point can also be found by solving the equations algebraically, but since this is a graphical method, you can visually locate it on the graph.

### Approximate Solution

From the calculations and plotted points, you can see that both equations have the common point:
- (-5, -7)

Thus, **the solution to the system of equations** is approximately at the point:
- **(-5, -7)**.

### Conclusion

Plot the points for each line, draw the lines, and look for their intersection. The solution point is (-5, -7).