Download presentation

Presentation is loading. Please wait.

1
**Solving Systems of Equations by Elimination**

Solving by elimination can be done by addition or multiplication.

2
**Solving Systems of Equations by Elimination**

Solve by addition Ex) 3x – 5y = -16 2x + 5y = 31 Notice that there is an inverse here (-5y and 5y)

3
**Solving Systems of Equations by Elimination**

3x – 5y = -16 the -5y and 5y will cancel +2x + 5y = 31 add like terms 5x + 0 = 15 divide by 5 x = 3 Now substitute the 3 into either equation for x and solve for y. 3(3) – 5y = – 5y = -16 solve equation y = -25 y = 5 solution (3,5)

4
**Solving Systems of Equations by Elimination**

Solve by multiplication If there is not an inverse, you need to multiply one or both of the equations to make an inverse in the problem. Ex) 5x + 2y = 6 9x + 2y = 22

5
**Solving Systems of Equations by Elimination**

Solve by multiplication If there is not an inverse, you need to multiply one or both of the equations to make an inverse in the problem. Ex) 5x + 2y = x + 2y = 6 9x + 2y = (9x + 2y = 22) Now eliminate the 2y and -2y

6
**Solving Systems of Equations by Elimination**

Solve by multiplication If there is not an inverse, you need to multiply one or both of the equations to make an inverse in the problem. Ex) 5x + 2y = x + 2y = 6 -1(9x + 2y = 22) x – 2y = -22 Now eliminate the 2y and -2y

7
**Solving Systems of Equations by Elimination**

Ex) 5x + 2y = 6 -9x – 2y = x = -16 x = 4 Now substitute the 4 in for x and solve for y 5(4) + 2y = y = 6 2y = -14 y = -7 solution (4, -7)

8
**Solving Systems of Equations by Elimination**

Ex) 3x + 4y = 6 5x + 2y = -4

9
**Solving Systems of Equations by Elimination**

Ex) 3x + 4y = 6 5x + 2y = -4 Sometimes, there is nothing obvious to inverse, you may have to multiply one or both equations by a number to inverse. 3x + 4y = 6 3x + 4y = 6 -2(5x + 2y = 4) -10x – 4y = 8

10
**Solving Systems of Equations by Elimination**

3x + 4y = 6 -10x – 4y = 8 -7x = 14 x = -2 3(-2) + 4y = y = 6 4y = 12 y = 3 solution (-2,3)

11
**Solving Systems of Equations by Elimination**

Ex) -3x – 3y = x + 8y = 16

12
**Solving Systems of Equations by Elimination**

Ex) -3x – 3y = x + 8y = 16 When neither equation has anything in common, you will have to multiply BOTH equations to find an inverse. -2(-3x – 3y = -21) 6x + 6y = 42 3(-2x + 8y = 16) -6x + 24y = 48

13
**Solving Systems of Equations by Elimination**

6x + 6y = 42 -6x + 24y = 48 30y = 90 y = 3 6x + 6(3) = 42 6x + 18 = 42 6x = 24 x = 4 solution (4, 3)

14
**Solving Systems of Equations**

Ex) 3x – 6y = 10 x – 2y = 4

15
**Solving Systems of Equations with No Solution**

Ex) 3x – 6y = 10 x – 2y = 4 Make inverse 3x – 6y = 10 3x – 6y = 10 -3(x – 2y = 4) -3x + 6y = = -2 0 ≠ -2 therefore, there is no solution

16
**Solving Systems of Equations**

Ex) 3x + 6y = 24 -2x – 4y = -16

17
**Solving Systems of Equations with Infinite Solutions**

Ex) 3x + 6y = 24 -2x – 4y = -16 Find the inverse 2(3x + 6y = 24) 6x + 12y = 48 3(-2x – 4y = -16) -6x – 12y = = 0 0 = 0 is a true statement, there are infinite solutions. They would graph as the same line.

18
**Solving Systems of Equations**

Method Best time to use Graphing *to estimate a solution Substitution *when one variable has a coefficient of 1 or -1 Elimination *when one of the variables has the same or opposite coefficients. *when there are no other options for solving.

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