Download presentation

1
**Solving Systems of Equations**

Section 4.2

2
**Useful when all variable have coefficients other than 1.**

Substitution Method (Windshield Wipers) Linear Combinations (Elimination) Useful technique for solving systems in which a variable has a coefficient of 1. Useful when all variable have coefficients other than 1. Step 1: Solve one of the equations for either one of its variables. Step 2: Substitute the expression you have for Step 1 into the other equation and solve for the remaining variable. Step 3: Substitute the value from Step 2 back into the equation from Step 1 and solve for the second variable. Step 4 : Check your solution in both of the original equations. Step 1: Arrange both equations so the like terms line up in same column. Step 2: Multiply one or both of the equations by the same number so the coefficients of one of the variables are additive inverses. Step 3: Add the equations together. One of the variables should eliminate because the coefficients will add to zero. Step 4: Solve for the remaining variable. Step 5: Substitute the solution from Step 4 Into either of the original equations and solve for the other variable. Step 6 : Check your solution in both of the original equations.

3
**Substitution Method (1, 8) y = 3x + 5 2x + 4y = 34 y = 3x + 5**

4
**Substitution Method (1, ) x – 4y = -1 2x + 2y = 3 x - 4y = -1**

2(4y-1) + 2y = 3 8y – 2 + 2y = 3 10y – 2 = 3 x = 10 y = 5 x = 2 - 1 y = x = 1 (1, )

5
**Decide which variable you want to eliminate.**

Linear Combination 3x – 5y = 14 2x + 4y = -20 I think I’ll choose to eliminate the y variable. Decide which variable you want to eliminate.

6
**Linear Combination 4 5 (-2, -4) 3x – 5y = 14 2x + 4y = -20**

7
**Decide which variable you want to eliminate.**

Linear Combination 2x + 7y = 48 3x + 5y = 28 I think I’ll choose to eliminate the x variable. Decide which variable you want to eliminate.

8
**Linear Combination 3 -2 (-4, 8) 2x + 7y = 48 3x + 5y = 28**

9
**Decide which variable you want to eliminate.**

Linear Combination 4x + 3y = -19 6x + 5y = -32 I think I’ll choose to eliminate the x variable. Decide which variable you want to eliminate.

10
**Linear Combination 3 -2 4x + 3y = -19 6x + 5y = -32 12x + 9y = -57**

11
**Substitution Method Parallel Lines y = -2x - 6 6x + 3y = 11**

- 18 = 11 Parallel Lines

12
**Infinitely many solutions**

Substitution Method x = 5y + 1 2x y = 2 2(5y + 1) y = 2 10y y = 2 2 = 2 Infinitely many solutions same lines

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