Download presentation

Presentation is loading. Please wait.

Published byDina Webster Modified over 9 years ago

1
Directions: Solve the linear systems of equations by graphing. Use the graph paper from the table. Tell whether you think the problems have one solution, no solution, or infinite solutions. EXAMPLE 3 a. 5x + y = –2 –10x – 2y = 4 Do Now: b. 6x + 2y = 3 6x + 2y = –5

2
Special Types of Systems: One Solution – Different Slopes No Solution – Same Slope; Different y – intercepts Infinite Solutions – Same slope; same y-intercept

3
Objective: To solve systems of linear equations using elimination by multiplying first.

4
SOLUTION EXAMPLE 1 Multiply one equation, then add Solve the linear system: 6x + 5y = 19 Equation 1 2x + 3y = 5 Equation 2 STEP 1 Multiply Equation 2 by –3 so that the coefficients of x are opposites. 6x + 5y = 19 2x + 3y = 5 6x + 5y = 19 STEP 2 Add the equations. –4y = 4 –6x – 9y = –15

5
EXAMPLE 1 Multiply one equation, then add STEP 3 STEP 4 2x = 8 Write Equation 2. 2x + 3(–1) = 5 Substitute – 1 for y. 2x + 3y = 5 x = 4 Multiply. Subtract – 3 from each side. Solve for y. Substitute –1 for y in either of the original equations and solve for x. 2x + (–3) = 5 Divide each side by 2. y = –1

6
EXAMPLE 1 Multiply one equation, then add ANSWER The solution is (4, –1). CHECK Equation 2 2x + 3y = 5 Substitute 4 for x and –1 for y in each of the original equations. Equation 1 6x + 5y = 19 6(4) + 5(–1) = 19 ? 2(4) + 3(–1) = 5 ? 19 = 19 5 = 5

7
EXAMPLE 2 Multiply both equations, then subtract Solve the linear system: 4x + 5y = 35 Equation 1 2y = 3x – 9 Equation 2 SOLUTION STEP 1 4x + 5y = 35 Write Equation 1. –3x + 2y = –9 Rewrite Equation 2. Arrange the equations so that like terms are in columns.

8
EXAMPLE 2 Multiply both equations, then subtract STEP 2 4x + 5y = 35 –3x + 2y = –9 23x = 115 STEP 3 STEP 4 8x + 10y = 70 –15x +10y = –45 Multiply Equation 1 by 2 and Equation 2 by 5 so that the coefficient of y in each equation is the least common multiple of 5 and 2, or 10. Subtract: the equations. x = 5 Solve: for x.

9
EXAMPLE 2 Multiply both equations, then subtract STEP 5 4x + 5y = 35 4(5) + 5y = 35 y = 3 Write Equation 1. Substitute 5 for x. Solve for y. ANSWER The solution is (5, 3). Substitute 5 for x in either of the original equations and solve for y.

10
EXAMPLE 2 Multiply both equations, then subtract CHECK 4x + 5y = 35 ANSWER The solution is (5, 3). Substitute 5 for x and 3 for y in each of the original equations. 4(5) + 5(3) = 35 ? Equation 1 Equation 2 2y = 3x – 9 2(3) = 3(5) – 9 ? 35 = 35 6 = 6

11
GUIDED PRACTICE for Examples 1 and 2 Solve the linear system using elimination. –2x + 3y = –5 6x – 2y = 11. ANSWER The solution is (–0.5, –2).

12
GUIDED PRACTICE for Examples 1 and 2 3x + 10y = –3 2x + 5y = 32. ANSWER The solution is (9, –3). Solve the linear system using elimination.

13
GUIDED PRACTICE for Examples 1 and 2 9y = 5x + 5 3x – 7y = 5 3. Solve the linear system using elimination. ANSWER The solution is (–10, –5).

Similar presentations

© 2024 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