Download presentation

Presentation is loading. Please wait.

1
**Solving Linear Systems by Linear Combinations**

7.3 Solving Linear Systems by Linear Combinations Objective 1 – Use linear combinations to solve a system of linear equations. Steps to solve systems with linear combination. 1. Arrange equations with like terms in columns. 2. Combine like terms to get a variable to cancel. 3. Solve for one of the variables 4. Use the solution in step 3 to find the other variable.

2
Example 3x – 2y = 1 2x + 2y = 4 Combine like terms in columns. The y’s cancel 5x = 5 Divide by 5 x = 1 Now substitute 1 for x in one of the original equations to solve for y. 2x + 2y = 4 2(1) +2y = 4 2 + 2y = 4 2y = 2 y = 1 Solution is (1,1)

3
**EXAMPLE x + 4y = 23 – x + y = 2 Combine like terms 5y = 25 y = 5**

Use y = 5 to solve for x x + 4y = 23 x + 4(5) = 23 x + 20 = 23 x = 3 Solution (3, 5)

4
**EXAMPLE Using Multiplication x – y = –5 x + 2y = 4**

Nothing Cancels! We must multiply one of the equations by a value to get opposites Multiply one equation by by -1 – x + y = 5 x + 2y = 4 –1(x – y = –5) x + 2y = 4 3y = 9 y = 3 x – y = –5 x – 3 = – 5 Solution (-2, 3) x = – 2

Similar presentations

© 2022 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