Download presentation

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

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google