Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Multivariable.

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Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Multivariable Linear Systems (Section 7-3)

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solving Using Back Substitution If you are given a system of equations in which one equation has 3 variables, one equation has 2 of those variables, and the third equation has 1 variable, you should solve by plugging the known variable into the equation with 2 variables. This will give you 2 variables, to complete solving plug the 2 known variables into the equation with 3 variables.

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 1 x – 2y + 3z = 9 y + 4z = 7 z = 2

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 2 x + y – 3z = -1 -y – z = 0 -x + 2y = 1

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Elimination Method to Solve a System in Three Variables 1)Use the elimination method to rewrite the system as a linear system in two variables. 2) Solve the system of two equations for both of the variables. 3) Subsitute the two values found in step 2 into one of the equations and solve for the last variable.

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 3 x – 2y + 3z = 9 -x + 3y + z =-2 2x – 5y + 5z = 17

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 4

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 5 x + y – z = 3 2x – y – z = 1 x + y – 2z = 5

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 6 x – 3y + z = 1 2x - y - 2z = 2 x + 2y – 3z = -1

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Use Cramer’s Rule to solve the linear system. Example 7

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Use Cramer’s Rule to solve the linear system. Example 8

Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. HW #43 pg (1, 7, odd)