System of Equations Substitution Method Presented Mr Laws

System of Equations Substitution Method Presented Mr. Laws Math I, JCMS

Standard/Goal • A. REI. 5– Explain why replacing one equation in a system of linear equations by the sum of that equation and multiple of the other produces a system with the same solution. • A-REI. 6 – Use tables, graphs, or algebraic methods (substitution and elimination) to find approximate or exact solutions to systems of linear equations and interpret solutions in terms of a context.

Essential Questions • Using math principles, how do I solve a system of equations using the substitution method?

Target Statement • I CAN solve a various system of equations using the substitution method?

What is the Subsitution Method? 1. A System of Equations are two or more equations. o Both equations can be written in slope intercept form or standard form or a combination of both forms. 2. When a system has at least one equation that can be solved quickly for a variable, the system can be solved efficiently using substitution. 3. You can solve an equation for one variable by substituting the expression for the variable into the other equation. This is called the substitution method.

Solving System by Substitution Example # 1 Step 1 – Take a look at the variables of both equations. y = 3 x x + y = -32 Step 2 – Since y = 3 x substitute 3 x for y in x + y = -32, . x + 3 x = -32 4 4 x = -8 y = 3(-8) y = -24 (-8, -24) Step 3 – Combine like terms and solve for x. Step 4 – Substitute -8 for x in either equation and solve for y. Step 5– Write the solution and check to see if it makes both equations true.

Solving System by Substitution Example # 2 3 y + 4 x = 21 -2 x + y = -3 +2 x y = 2 x – 3 3(2 x – 3) + 4 x = 21 6 x – 9 + 4 x = 21 Step 1 – Take a look at the variables of both equations. Step 2 – Solve one equation for one of the variables. Solve for y for equation -2 x + y = -3 Step 3 – Substitute 2 x – 3 for y in other equation and solve for x. Step 4 – Use the distributive property and combine like terms. .

Solving System by Substitution Example # 2 Step 5 – Combine like terms and solve for x. 6 x – 9 + 4 x = 21 10 x – 9 = 21 +9 +9 10 x = 30 10 10 Step 6 – Substitute 3 for x in other equation and solve for y. x=3 3 y + 4(3) = 21 3 y + 12 = 21 - 12 3 y = 9 3 3 Step 7 – Write the solution and check to it with any equation. (3, 3) y=3

Solving System by Substitution Example # 3 A snack bar sells two sizes of snack packs. A large snack pack is $5, and a small snack pack is $3. In one day, the snack bar sold 60 snack packs for a total of $220. How many small snack packs did the snack bar sell? Let x = # of large $5 snack packs. Let y = # of small $3 snack packs. Step# 1: Write a system of equation based on the information given. 1 st Equation: x + y = 60 (total # of snack packs 2 nd Equation: 5 x + 3 y = 220 (the amt made from selling 60 snack packs. x + y = 60 -x -x y = -x + 60 Step#2: Use 1 st equation to solve for y.

Solving System by Substitution Example # 3 A snack bar sells two sizes of snack packs. A large snack pack is $5, and a small snack pack is $3. In one day, the snack bar sold 60 snack packs for a total of $220. How many small snack packs did the snack bar sell? Step# 3: Substitute –x + 60 for y 5 x + 3(-x +60) = 220 in the second equation. 5 x -3 x + 180 = 220 Step# 4: Simplify using distributive property and combining like terms. 2 x + 180 = 220 -180 2 x = 40 2 2 20 + y = 60 -20 y = 40 x = 20 Step# 5: Solve for x. Step# 6: Substitute 20 for x in other equation to find y. Solve for y. (20, 40) The snack bar sold 40 small snack packs.

Your Turn Solve each System using substitution method. Show your work! 1. ) x+y=8 y = 3 x 2. ) y – 2 x = 3 3 x – 2 y = 5 3. ) 4 x = 3 y – 2 18 = 3 x + y 4. ) You pay $22 to rent 6 video games. The store charges $ 4 for new games and $2 for older games. How many new games did you rent? a. b. c. d. 5 new games 6 new games 11 new games 12 new games

Summary • What have you learned in this lesson? • What are some important things to remember about system of equations? • Do you have additional questions concerning this lesson?