1. 5.1 Solving Systems of Equations by Graphing
Objectives:
To find the solution of a system of equations by graphing

2. Warmup

3. A System of linear equations is a set of two or more linear equations
Example: y = 2x + 5 and 3x +2y =12
A solution of a system of equations is an ordered pair that is a solution to each equation (x,y)

4. Example 1 Solve the following system by graphing. x + y = 2 x = y x y2 -8 -6 -4 -2 2 4 6 8 1 1 5 -3
(1,1)
x = y x y 1 1 5 5

5. Practice Solve by graphing. x + 4y = -6 2x – 3y = -1 y + 2x = 5

6. Example 2 Determine whether (3,5) is a solution of the system.
y = 4x - 7
x + y = 8
5 =
4( ) 3
- 7 3
+ 5
= 8
5 =
8 = 8
5 = 5
(3,5) is a solution of the system

7. Example 3 Determine whether (-2,1) is a solution of the system.
2x – y = -5
3x + 2y = 3
2( ) -2
- 1
= -5
3( ) -2
+ 2( ) 1
= 3
-4 – 1 = -5
= 3
-5 = -5
(-2,1) is not a solution of the system

8. Practice
Determine whether the given ordered pair is a solution of the system.
(2,-3); x = 2y + 8
2x + y = 1
(-3,4); 2x = -y – 2
y = -4

9. Practice
Solve these system by graphing.
Y + 2x = 5
2y – 5x =10