Download presentation

Presentation is loading. Please wait.

Published byIsaac Brown Modified over 8 years ago

1
Solving Systems Using Elimination Objective: To solve systems of equations algebraically

2
System of Equations Remember: – 2 or more equations that use the same 2 or more variables. – Solved by graphing and substitution Now … We have elimination - Just another method of solving systems

3
Solving By Elimination Also Known as the Addition/Subtraction Method You’re going to ELIMINATE one of the two variables Solve for the 2 nd variable Use the solution of the 2 nd variable to solve for the 1 st. Answer comes in an ordered pair: (x, y)

4
Example #1 2x + 5y = 17 6x – 5y = -9 Step #1: Align Equals Sign Step #2: Align Variables Step #3: Ask yourself “ If I add/subtract vertically, does something get eliminated?”

5
Example #1 2x + 5y = 17 6x – 5y = -9 8x = 8 YES!!! Now, solve for x 8x = 8 8 8 x = 1

6
x = 1 2x + 5y = 17 2(1) + 5y = 17 2 + 5y = 17 -2 5y = 15 5 5 y = 3 Now plug 1 in for x and solve for y in either equation Our Solution is (1, 3)

7
Example #2 2x +5y = -22 10x + 3y = 22 Step #1: Align Equals Step#2: Align Variables Step #3: Ask Yourself “If I add/subtract vertically, does something get eliminated?”

8
Example #2 2x +5y = -22 10x + 3y = 22 12x + 8y = 0 2x +5y = -22 10x + 3y = 22 -8x + 2y = -44 Nothing gets eliminated by adding … Try Subtracting Nothing there, either. What to do?

9
Example #2 2x +5y = -22 10x + 3y = 22 5 (2x + 5y) = 5(-22) 10x + 25y = -110 10x + 3y = 22 If you multiply the top equation by 5 … would that simplify things? Don’t forget to multiply both sides. How about now? Can something get eliminated?

10
Example #2 10x + 25y = -110 10x + 3y = 22 22y = -132 22 22 y = -6 10x + 3(-6) = 22 10x – 18 = 22 + 18 +18 10x = 40 10 x = 4 Yes! By Subtraction. Solve for y Now, plug in the answer to y in either equation Solve for x Our solution is (4, -6)

11
Example #3 2x + 5y = 18 3x - 4y = 4 Step #1: Align equals sign Step #2: Align variables Step #3: Ask yourself If you add/subtract vertically, does something get eliminated?

12
Example #3 2x + 5y = 18 3x - 4y = 4 5x + y = 22 2x + 5y = 18 3x - 4y = 4 -x + 9y = 14 Nothing gets eliminated by adding. Nothing gets eliminated by subtracting either

13
Example #3 2x + 5y = 18 3x - 4y = 4 3(2x + 5y) = 3(18) 2(3x – 4y) = 2(4) 6x + 15y = 54 6x – 8y = 8 In this system, both equations must be multiplied. We’re going to multiply the 1 st equation by 3 and the 2 nd equation by 2 Now we can subtract!!!

14
Example #3 6x + 15y = 54 6x – 8y = 8 23y = 46 23 23 y = 2 2x + 5y = 18 Don’t forget 15 – (-8) is 23. Now solve for x. This is one of our original equations

15
Example #3 2x + 5y = 18 2x + 5(2) = 18 2x + 10 = 18 -10 -10 2x = 8 2 x = 4 Replace y with 2 Subtract 10 from both sides Divide by 2 Our Solution is (4,2)

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