1. 3.1 Solving Linear Systems by Graphing
10/1/12

2. Vocabulary System of 2 Linear Equations:
A system consisting of two linear
equations in two variables.
Ex: 6x – 2y = 8
3x – y = 4
Solution of a system of 2 linear equations:
Is an ordered pair (x, y) that satisfies both equations.
Graphically, it’s the point where the lines intersect.

3. Tell whether the ordered pair (3, 4) is a solution of
-2x + y = -2
4x – 2y = 3
Substitute 3 for x and 4 for y in BOTH equations.
-2(3) + 4 = -2
= -2
4(3) – 2(4) = 3
12 – 8 = 3
Answer: Not a Solution

4. Answer: Solution Tell whether the ordered pair (3, 4) is a solution of
x + 2y = 11
2x – y = 2
Substitute 3 for x and 4 for y in BOTH equations.
3 + 2(4) = 11
3 + 8 = 11
2(3) – 4 = 2
6 – 4 = 2
Answer: Solution

5. Solve the system by graphing. Then check your solution.
Example 1
Solve a System by Graphing
Solve the system by graphing. Then check your solution. 3 y – x = + 9 y 2 x = +
ANSWER ( )
2, 5 –

6. y = - x + 3 5= -(-2) + 3 5= 5 y = 2 x + 9 5 = 2(-2) + 9 5 = -4 + 9
You can check the solution by substituting -2 for x and 5 for y into the original equations.
y = - x + 3
5= -(-2) + 3
5= 5
y = 2 x + 9
5 = 2(-2) + 9
5 =
5 = 5

7. Solve the system by graphing. Then check your solution algebraically.
Example 2
Solve a System by Graphing
Solve the system by graphing. Then check your solution algebraically. 3 3x – y =
In slope int. form: y = 3x - 3 8 x + 2y =
ANSWER ( )
2, 3
In slope int. form: y = x + 4

8. The solution of the system is
Example 2
Solve a System by Graphing
You can check the solution by substituting 2 for x and 3 for y into the original equations.
Equation 1
Equation 2 3 3x – y = 8 x + 2y ( ) 2 3 – = ? 8 + 3 6 – = ? 2 8 + 3 = 8
ANSWER ( ).
2, 3
The solution of the system is 8

9. Extra Example
Solve the system by graphing. Then check your solution. 1. x 3y = – 1 x y = + 1 –
ANSWER ( )
1, 0

10. Solve the system by graphing. Then check your solution.
Checkpoint
Solve a System by Graphing
Solve the system by graphing. Then check your solution. 2. 2 + 4y x – = 2x 3y = – 6
ANSWER ( )
6, 2

11. Homework
WS 3.1

12. Number of Solutions 1 solution : the lines have different slopes
Infinitely many solutions
:the lines have the same equation.
No solution
:the lines are parallel (same slope)

13. Tell how many solutions the linear system has.
Example 3
Systems with Many or No Solutions
Tell how many solutions the linear system has. b. + = 2y x 1 4 a. 1 = y – 2x + = 2y – 4x 2
Infinitely many solutions
:the lines have the same equation.
No solution
:the lines are parallel (same slope)

14. Tell how many solutions the linear system has.
Checkpoint
Write and Use Linear Systems
Tell how many solutions the linear system has. 3. + = 3y 2x 1 6y 4x 3
ANSWER 4. 5 = 4y – x +
ANSWER
infinitely many
solutions 5. 5 = 5y – x +
ANSWER 1