Core Focus on Linear Equations Lesson 4.6 Core Focus on Linear Equations Choosing the Best Method

Warm-Up Solve one of the systems below using any method. Explain why you chose your method. y = 5x – 4 x + 2y = 25 2x + 7y = 1 –2x + 2y = –10 y = x – 4 y = –3x + 3 (3, 11) (4, −1) (2, −3)

Choosing the Best Method Lesson 4.6 Choosing the Best Method Choose the best method for solving a given system of equations.

Good to Know! GRAPHING TABLES SUBSTITUTION ELIMINATION A quick review of the four methods you have learned to solve systems of linear equations. GRAPHING Graph both equations in slope-intercept form. Identify their point of intersection. TABLES Create an input-output table for each equation using the same input values. Locate the point in each table where the same pair of input and output values occur. SUBSTITUTION Solve for a variable in one equation and substitute that expression into the other equation. Solve that equation for one variable. Substitute the solution into one of the original equations to solve for the second variable. ELIMINATION Create opposite coefficients on one variable in the two equations. Add equations together to eliminate one variable. Solve for the remaining variable. Substitute the solution into one of the original equations to solve for the second variable.

Explore! What’s Easiest? Nate and Tabi were given five systems of equations to solve. Their teacher told them each system could be solved using any of the four methods from the previous slide. For each one, however, there is one method that would be the easiest to use. Step 1 Tabi likes elimination the best so she decides that she will solve them all with elimination. Her teacher said one of the systems is set up for elimination. Which system do you think the teacher referred to? Why? Step 2 Nate believes substitution is always the easiest method to use, no matter how the system is set up. The teacher told Nate there are two systems set up in a way that will make substitution the easiest method for solving. Which two systems do you think the teacher was talking about and why? Step 3 Two systems are left. Which one would you solve by graphing? Which one would you solve using input-output tables? Explain your reasoning. Step 4 Choose one of the systems above and find the solution.

Choosing a Method to Solve a System of Linear Equations Graphing: If both equations are in slope-intercept form, graphing is an appropriate method to use. Tables: If both equations are in slope-intercept form and the slope is an integer, input-output tables may be a good method. Substitution: If a variable is isolated in one equation, substitution will most likely be the best method. Elimination: If the two equations in the system are in standard form and the variables are lined up in columns, elimination may be the easiest method.

Example 1 Choose the best method to solve the system of equations. Explain your reasoning. a. x – 2y = 10 3x + 2y = 6 The best method for solving this system of linear equations would be ELIMINATION. This method would be easiest because the variables are already lined up in columns and the y-variable is already set to be eliminated when the two equations are added together.

Example 1 Continued… Choose the best method to solve the system of equations. Explain your reasoning. b. y = 2x – 3 4x – 5y = –1 The best method for this system is SUBSTITUTION. The y-variable in the first equation is isolated on one side of the equals sign which provides an expression to substitute into the other equation and solve.

Example 1 Continued… Choose the best method to solve the system of equations. Explain your reasoning. c. y = x y = 2x + 7 Both equations are solved for y which allows this to be easily solved by GRAPHING. Remember that when the graphing method is used, it is important to verify the solution by substituting the x- and y-values back into both equations.

Example 1 Continued… Choose the best method to solve the system of equations. Explain your reasoning. d. y = 5x – 9 y = 2x – 3 Both equations are in slope-intercept form. The slope in each equation is an integer. The best method for solving this system of equations may be TABLES.

Communication Prompt Choose one method for solving a system of equations. Describe how the equations might be set up to allow you to easily solve it with your method.

Exit Problem Write a sample of a system of equations that would be best solved by… a) elimination b) graphing c) substitution