1 / 7

Understanding Substitution in Systems of Linear Equations

This guide delves into the substitution method for solving systems of linear equations. It describes three main techniques: substitution, elimination, and graphing, focusing on substitution today. You'll learn how to solve one equation for a variable, substitute it into another equation, and then solve for both variables. We also explore the types of solutions possible: one solution, no solution, and infinitely many solutions, providing examples for each category. Try solving some practice problems to enhance your understanding!

jaser
Télécharger la présentation

Understanding Substitution in Systems of Linear Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Systems of Linear Equations Substitution

  2. Linear Equations • There are 3 different ways to solve linear equations: • 1. Substitution • 2. Elimination • 3. Graphing • We will focus on a new one each day. • Today is Substitution.

  3. Substitution • Substitution is just what it sounds like. • Rewrite one equation and substitute it into the other equation. • x + y = 270 • 6x + 8y = 2080 • y = 270 – x • 6x + 8(270 – x) = 2080 • 6x + 2160 – 8x = 2080 • 2160 – 2x = 2080 • - 2x = - 80 • x = 40 • y = 270 – 40 • y = 230 • (40, 230) Solve one equation for a single variable. Substitute the “new” equation into the 2ns equation. Solve for the variable. Plug that answer back into one of the equations and solve for the 2nd variable.

  4. Substitution • When solving systems of equations, solutions will fall into one of three categories. • 1. One Solution • 2. No solution • 3. Infinitely many solutions • One solution means that the lines cross one time. That is the intersection we are solving for. • No solution means the lines never cross….parallel lines. • Infinitely many solutions means the equations are for the same lines.

  5. Substitution • Solve: • x – y = 2 • 2x – 2y = 10 • x = 2 + y • 2(2 + y) – 2y = 10 • 4 + 2y – 2y = 10 • 4 = 10 ??? • This is no solution because 4 does not equal 10.

  6. Substitution • Solve: • x – y = 2 • - x + y = - 2 • x = 2 + y • - (2 + y ) + y = - 2 • - 2 – y + y = - 2 • - 2 = - 2 • This is true, so infinitely many solutions.

  7. Substitution • Your turn to try a few! • 2x + y = 3 x – y = 2 x + 2y = 1 • 4x + 2y = 4 4x – 3y = 10 2x + 4y = 2 • No Solution (4, 2) Infinitely many solutions

More Related