To solve the system of equations graphically, we will plot the two equations on a graph.
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The first equation is \( y = -\frac{1}{2}x + 7 \).
- This line has a slope of -1/2 (downward) and a y-intercept of 7.
- You can plot this by starting at the point (0, 7) on the y-axis, and then going down 1 unit for every 2 units you move to the right.
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The second equation is \( y = \frac{3}{2}x - 5 \).
- This line has a slope of 3/2 (upward) and a y-intercept of -5.
- You can plot this by starting at the point (0, -5) on the y-axis, and then going up 3 units for every 2 units you move to the right.
Steps to Graph:
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Plotting the First Line (\(y = -\frac{1}{2}x + 7\)):
- Y-intercept: (0, 7)
- Another point: For \(x = 2\), \(y = -\frac{1}{2}(2) + 7 = 6\) → Point (2, 6)
- Draw the line passing through (0, 7) and (2, 6).
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Plotting the Second Line (\(y = \frac{3}{2}x - 5\)):
- Y-intercept: (0, -5)
- Another point: For \(x = 2\), \(y = \frac{3}{2}(2) - 5 = -2\) → Point (2, -2)
- Draw the line passing through (0, -5) and (2, -2).
Finding the Intersection Point:
The solution to the system of equations is the point where the two lines intersect.
After you finish plotting the lines, look for the point where they cross. You may calculate the intersection algebraically by setting the two equations equal to each other:
\[ -\frac{1}{2}x + 7 = \frac{3}{2}x - 5 \]
Solving this equation will give you the x-coordinate of the intersection point. Substitute this back into either original equation to find the y-coordinate.
Final Note:
Since I cannot directly interact with a graphing utility, please use a graphing tool or graphing paper to carry out these instructions visually!