Question

Solve this system of equations by graphing. First graph the equations, and then type the solution.

y = 7/2x - 3

y = -3/2x + 7

Answer 1

To solve the system of equations by graphing, we can start by graphing each equation.

1. **Graphing the first equation:**
\[
y = \frac{7}{2}x - 3
\]
- This equation is in slope-intercept form \(y = mx + b\), where the slope \(m = \frac{7}{2}\) and the y-intercept \(b = -3\).
- To find another point, we can substitute \(x = 2\) into the equation:
\[
y = \frac{7}{2}(2) - 3 = 7 - 3 = 4 \quad \Rightarrow \quad (2, 4)
\]
- The first two points to graph are (0, -3) and (2, 4).

2. **Graphing the second equation:**
\[
y = -\frac{3}{2}x + 7
\]
- This equation is also in slope-intercept form, where the slope \(m = -\frac{3}{2}\) and the y-intercept \(b = 7\).
- To find another point, we can substitute \(x = 2\):
\[
y = -\frac{3}{2}(2) + 7 = -3 + 7 = 4 \quad \Rightarrow \quad (2, 4)
\]
- The first two points to graph are (0, 7) and (2, 4).

Now, we can plot these points on a graph and draw the lines for each equation.

- The first line described by \(y = \frac{7}{2}x - 3\) rises steeply and goes through the points (0, -3) and (2, 4).
- The second line described by \(y = -\frac{3}{2}x + 7\) is decreasing, going through (0, 7) and also (2, 4).

Notice that both lines intersect at the point (2, 4).

### Solution
The solution to the system of equations is:
\[
\boxed{(2, 4)}
\]