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Graph of x + 2y - 7 = 0 and 2x - y - 4 = 0
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Equations:
- x + 2y - 7 = 0
- 2x - y - 4 = 0
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Graphing the Equations:
- To graph these equations, first, rearrange them in slope-intercept form (y = mx + b).
- For the first equation, x + 2y - 7 = 0, we have 2y = -x + 7, then y = -0.5x + 3.5.
- For the second equation, 2x - y - 4 = 0, we have y = 2x - 4.
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Plotting the Points:
- Plot at least two points for each equation to draw the lines on the graph.
- For y = -0.5x + 3.5, you can plot points like (0, 3.5) and (7, 0).
- For y = 2x - 4, you can plot points like (0, -4) and (2, 0).
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Drawing the Lines:
- Use a ruler to draw the lines passing through the points you plotted for each equation.
- The lines will intersect at a point which is the solution to the system of equations.
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Intersecting Point:
- The point where the two lines intersect is the solution to the system of equations.
- You can find the coordinates of this point by solving the system of equations simultaneously.
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Conclusion:
- By following these steps, you can graph the equations x + 2y - 7 = 0 and 2x - y - 4 = 0 and find the intersecting point, which represents the solution to the system of equations.