To solve the system of equations by graphing, we can start by graphing each equation.
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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).
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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: \[ \boxed{(2, 4)} \]