Download presentation

Presentation is loading. Please wait.

Published byDonna Preston Modified over 4 years ago

1
Solving Linear Systems By Elimination

2
Solving Linear Systems There are three methods for solving a system of equations: By Graphing them and looking at the results By solving them algebraically using Elimination By solving them algebraically using Substituion

3
Elimination ● The key to solving a system by elimination is getting rid of one variable. ● Let’s review the Additive Inverse Property. ● What is the Additive Inverse of: 3x? -5y? 8p? -3x 5y -8p ● What happens if we add two additive inverses? We get zero. The terms cancel, therefore Eliminating them.

4
The Elimination Method ● We will try to eliminate one variable by adding, subtracting, or multiplying the variable(s) until the two terms are additive inverses. ● We will then add the two equations, giving us one equation with one variable. ● Solve for that variable. ● Then insert the value into one of the original equations to find the other variable.

5
Solving a System by Elimination ● Solve the system: x + y = 7 x - y = 5 ● Notice that the y terms in both equations are additive inverses. So if we add the equations the y terms will cancel. ● So let’s add & solve:x + y = 7 + x - y = 5 2x + 0 = 12 2x = 12 x = 6 ● Insert the value of x to find y: 6 + y = 7 so y = 1 The solution is (6, 1).

6
Solving a System by Elimination ● Solve the system: 2x + 3y = 23 x - 3y = -11 ● Notice that the y terms in both equations are additive inverses. So if we add the equations the y terms will cancel. ● So let’s add & solve:2x + 3y = 23 + x - 3y = -11 3x + 0 = 12 3x = 12 x = 4 ● Insert the value of x to find y: 2(4) + 3y = 23 so y = 5 The solution is (4, 5).

7
Another Elimination Example ● Solve the system: 3s - 2t = 10 4s + t = 6 ● What is the problem? There is NO additive inverse! ● We could multiply the second equation by 2 and the t terms would be inverses. Let’s multiply the second equation by 2 to eliminate t. 3s - 2t = 10 3s – 2t = 10 2(4s + t = 6) 8s + 2t = 12 ● Add and solve: 11s + 0 = 22 11s = 22 s = 2 ● Insert the value of s to find the value of t: 3(2) - 2t = 10 so t = -2 ● The solution is (2, -2).

8
Some to try: 1. -4x + y = -12 4x + 2y = 6 2.5x + 2y = 12 -6x -2y = -14 3.5x + 4y = 12 7x - 6y = 40 4.5m + 2n = -8 4m +3n = 2

Similar presentations

© 2019 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