1. Graphing Systems
of Equations

2. What is a System?
A system refers to two lines graphed on the same coordinate plane.
The solution to a system is the point or points that the two lines have in common.

3. Example System y = -x + 4 & y = x - 2
1) Graph both equations on the same plane.
A) y = -x + 4
y-int = 4
slope = -1/1

4. Example System (continued)
y = -x & y = x - 2
1) Graph both equations on the same plane.
B) y = x - 2
y-int = -2
slope = 1/1

5. Example System (continued)
y = -x & y = x - 2
2) If the lines intersect (cross), the solution is the intersection point.
What is this point?
(3, 1)

6. Example System (continued)
y = -x & y = x - 2
3) To check the solution, substitute the x and y values of the point into the x and y variables of the equations. Both equations should be balanced.
(3, 1)
A) y = -x + 4
1 = -(3) + 4
1 = 1 √

7. Example System (continued)
y = -x & y = x - 2
3) To check the solution, substitute the x and y values of the point into the x and y variables of the equations. Both equations should be balanced.
(3, 1)
B) y = x - 2
1 = 3 - 2
1 = 1 √

8. Example #2
y = -x & y = 3x + 6
1) Graph both equations on the same plane.
A) y = -x + 2
y-int = 2
slope = -1/1

9. Example #2 (continued) y = -x - 2 & y = 3x + 6
1) Graph both equations on the same plane.
B) y = 3x + 6
y-int = 6
slope = 3/1

10. Example #2 (continued) (-2, 0) y = -x - 2 & y = 3x + 6
2) What is the solution?
(-2, 0)
3) Check it:
A) y = -x - 2
0 = -(-2)- 2
0 = 2 - 2
0 = 0 √
B) y = 3x + 6
0 = 3(-2)+ 6
0 = (-6) + 6
0 = 0 √