6-5 Applying Systems of Linear Equation Objectives: Determine the best method for solving systems of equations. Apply systems of equations.

We’ve learned 5 methods to solve systems of linear equations We’ve learned 5 methods to solve systems of linear equations. The table summarizes the methods and types of systems for which each method works best. Solving Systems of Equations Method Best Time to Use Graphing When the equations are in slope-intercept form. To estimate solutions. Substitution If one of the variables in either equation has a coefficient of 𝟏 or −𝟏. Elimination (+) If one of the variables has opposite coefficients in the two equations. Elimination (-) If one of the variables has the same coefficient in the two equations. Elimination (×) If none of the coefficients are 𝟏 or −𝟏 and neither of the variables can be eliminated by simply adding or subtracting the equations.

Example 1: Determine the best method to solve each system. a) 5𝑥+7𝑦=2 −2𝑥+7𝑦=9 b) 3𝑥−4𝑦=−10 5𝑥+8𝑦=−2 c) 𝑦= 1 3 𝑥−4 𝑦=− 2 5 𝑥+2 d) 𝑥−𝑦=9 7𝑥+𝑦=7 e) 5𝑥−𝑦=17 3𝑥+2𝑦=5 f) 2𝑥−3𝑦=−12 𝑥=5𝑦−4

Example 2: Jared has volunteered 50 hours and plans to volunteer 3 hours in each upcoming week. Brian is a new volunteer who plans to volunteer 5 hours each week. Write and solve a system of equations to find how long it will be before they will have volunteered the same amount of hours.

Practice WS

Homework Page 367: 6-13