Solve the following system of equations graphically on the set of axes below: y = 2x - 2, x + y = 4.

Steps to Solve

1. Identify the equations We have the following equations to graph:

   • ( y = 2x - 2 )
   • ( x + y = 4 )

2. Convert the second equation to slope-intercept form The second equation needs to be rewritten in the form ( y = mx + b ): $$ y = 4 - x $$ This shows that the slope is (-1) and the y-intercept is (4).

3. Find points for the first equation To graph ( y = 2x - 2 ), we can find points by choosing values for ( x ):

   • If ( x = 0 ), then ( y = 2(0) - 2 = -2 ) → point (0, -2)
   • If ( x = 2 ), then ( y = 2(2) - 2 = 2 ) → point (2, 2)

4. Find points for the second equation To graph ( y = 4 - x ), find points:

   • If ( x = 0 ), then ( y = 4 - 0 = 4 ) → point (0, 4)
   • If ( x = 4 ), then ( y = 4 - 4 = 0 ) → point (4, 0)

5. Plot the points on a graph On the coordinate plane:

   • Plot the points (0, -2), (2, 2) for the first equation.
   • Plot the points (0, 4), (4, 0) for the second equation.

6. Draw lines between the points Connect the points you plotted for each equation to form straight lines.

7. Identify the intersection point The point where the two lines intersect represents the solution to the system of equations.