Solve the following system of linear equations by first graphing the system

y = 1/2x + 7
y = =2x - 2
(_,_)

1 answer

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).