Chapter 3: Linear Systems Section 3.2: Solving Systems Algebraically

Section 3.2: Solving Systems Algebraically Goal: To solve linear systems algebraically

Section 3.2: Solving Systems Algebraically Issue with graphing method? Unless the lines intersect at an exact point, the solution may have to be estimated Solution: use another method for exact solutions! Substitution Method Elimination Method (aka Linear Combination)

Section 3.2: Solving Systems Algebraically Substitution Method Solve for a variable Substitute expression into other equation and solve for the variable Substitute value of variable into the first equation and solve for remaining variable Check your solution!

Section 3.2: Solving Systems Algebraically Examples: What is the solution of the system of equations? 5x – 3y = -1 x + y = 3

Section 3.2: Solving Systems Algebraically Examples: What is the solution of the system of equations? 3g – 2h = -1 4g + h = 17

Section 3.2: Solving Systems Algebraically Examples: 3. You are in charge of ordering labels for a small business. A company that makes custom labels charges a yearly fee plus a cost per label. You paid $375 last year for 300 labels. This year you ordered 1000 labels and paid $725. What are the yearly fee and cost per label, assuming the prices did not change?

Section 3.2: Solving Systems Algebraically Homework (Part 1): Pg. 146 #10-20 (even)

Section 3.2: Solving Systems Algebraically Elimination Method (aka Linear Combination) Align the equations vertically Multiply one or both equations in order to have a variable be eliminated Add the equations and solve for the remaining variable Plug value into one of the original equations and solve for the other variable

Section 3.2: Solving Systems Algebraically Examples: What is the solution of the system of equations? 2x – 3y = 14 4x + 3y = 46

Section 3.2: Solving Systems Algebraically Examples: What is the solution of the system of equations? 7x + 5y = 2 8x – 9y = 17

Section 3.2: Solving Systems Algebraically Examples: What is the solution of the system of equations? 6x + 4y = 2 3x + 2y = -1

Section 3.2: Solving Systems Algebraically Examples: What is the solution to the system of equations? 6x – 3y = 15 -8x + 4y = -20

Section 3.2: Solving Systems Algebraically Homework (Part 2) Pg. 144 #22-42 (even)