To solve the system of equations by graphing, we first need to rewrite both equations in a suitable format for graphing.
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The first equation is: \[ x + 4y = -8 \] To express it in slope-intercept form \(y = mx + b\): \[ 4y = -x - 8 \ y = -\frac{1}{4}x - 2 \]
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The second equation is: \[ y = \frac{1}{2}x - 5 \]
Now, let's graph both equations:
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For the first equation \(y = -\frac{1}{4}x - 2\):
- When \(x = 0\), \(y = -2\) (the y-intercept).
- When \(x = -4\), \(y = -3\) (useful for plotting).
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For the second equation \(y = \frac{1}{2}x - 5\):
- When \(x = 0\), \(y = -5\) (the y-intercept).
- When \(x = 10\), \(y = 0\) (useful as a point).
Graphing the Equations:
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Graph the line of the first equation:
- Start at (0, -2) and draw a line through (-4, -3).
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Graph the line of the second equation:
- Start at (0, -5) and draw a line through (10, 0).
Finding the Intersection Point:
Once the two lines are graphed, find the coordinates where they intersect. This point represents the solution to the system of equations.
After graphing, you should see the intersection point. If we assume you've plotted correctly, let's approximate the intersection point.
Upon estimating or calculating the intersection, you might find:
- The intersection point is (x, y) = (2, -4).
Conclusion:
The solution to the system of equations is: \[ (x, y) = (2, -4) \]
If you require further assistance or visualization, you can use graphing software or a graphing calculator for accuracy.