To graph the system of equations, we first rewrite them in slope-intercept form (y = mx + b):
1) y = 1/2x + 7
This equation has a slope of 1/2 and y-intercept of 7.
2) y = 2x - 2
This equation has a slope of 2 and y-intercept of -2.
Now, we will graph both of these lines on the same coordinate plane:
For y = 1/2x + 7:
- Plot the y-intercept at (0,7)
- Use the slope to find another point, for example, go up 1 unit and right 2 units to get (2,8), and go down 1 unit and left 2 units to get (-2,6)
- Draw a line passing through these points
For y = 2x - 2:
- Plot the y-intercept at (0,-2)
- Use the slope to find another point, for example, go up 2 units and right 1 unit to get (1,0), and go down 2 units and left 1 unit to get (-1,-4)
- Draw a line passing through these points
The lines intersect at the point (2,6). Therefore, the solution to the system of equations is (2,6).
Solve the following system of linear equations by first graphing the system
y = 1/2x + 7
y = =2x - 2
(_,_)
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