Solving Systems of Equations By Substitution A-REI.3; A-REI.5; A-REI.6; A-REI.7

Table of Contents 46: Warm-Up 47: How Do I Solve a System of Equations by Substitution?

Warm-Up Solve the system of equations and state the solution as an ordered pair. Hint: Solve the equations for y 1. x + 2y = 6 g(x) = ½x - 1 2. h(x) = 2 -2x + 3y = -6

Warm-Up 1. x + 2y = 6 g(x) = ½x - 1 x + 2y = 6 - x - x _____________ __ 2 __ 2 __ 2 y = - ½x + 3 Solution: (4, 1)

Warm-Up 2. h(x) = 2 -2x + 3y = -6 +2x +2x _____________ __ 3 __ 3 3y = 2x – 6 __ 3 __ 3 y = 2x – 2 3 Solution: (6, 2)

Learning Intention/Success Criteria LI: We are learning how to solve a system of equations by substitution SC: I know how to -determine if a system of equations has many, none, or no solutions -solve systems of two linear equations algebraically using substitution method -solve equations for a variable

EQ: How Do I Solve a System of Equations by Substituting? 11/14/2018

Fold the paper in half, hot dog style Cut along the fold, making two strips of paper

Take one piece and lay it flat

Take the other piece of paper and place it on top of the first Take the other piece of paper and place it on top of the first. Make sure to leave a space at the bottom

Fold the second piece down and leave a space to writing

Fold the first piece down and leave a space to writing Staple Staple

Solving Systems with Substitution No Solutions Many Solutions One Solution

Open the foldable so that you can write on the one solution page

{ 3x + 2y = 10 x – 2y = 6 1. Solve an equation for a variable ___________ x = 2y + 6 One Solution

x = 2y + 6 2. Substitute eq 3. Substitute value x = 2y + 6 3x + 2y = 10 3x + 2y = 10 y = -1 3(2y + 6) + 2y = 10 3x + 2(-1) = 10 + 2y = 10 6y + 18 3x + -2 = 10 +2 +2 ____________ 8y + 18 = 10 3x = 12 __ 3 __ 3 x = 4 ____________ -18 -18 8y = -8 __ 8 __ 8 4. Solution: (4, -1) y = -1 One Solution

{ Guided Practice 1 Find the solution to the system by substitution: y = 2x – 4 x + 3y = 9 { x + 3y = 9 -2x + y = -4 x + 3(2x – 4) = 9 x = 3 -2x + y = -4 x + 6x - 12 = 9 -2x + y = -4 +2x +2x 7x – 12 = 9 __________ -2(3) + y = -4 +12 y = 2x - 4 ___________ +12 -6 + y = -4 7x = 21 __ 7 __ 7 +6 +6 ___________ (3, 2) One Solution y = 2 x = 3

Solving Systems with Substitution No Solutions Many Solutions One Solution

Open the foldable so that you can write on the many solution page Many Solutions One Solution

{ 4x - 2y = -10 -2x + y = 5 1. Solve an equation for a variable ____________ y = 2x + 5 Many Solutions One Solution

y = 2x + 5 2. Substitute eq 3. Answer 4x – 2y = -10 y = 2x + 5 Many Solutions When graphed, the lines are the same. 4x -2(2x + 5) = -10 4x - 4x - 10 = -10 0x – 10 = -10 – 10 = -10 Many Solutions One Solution

{ Guided Practice 2 Find the solution to the system by substitution: 9x – 3y = -15 y = 3x + 5 { 9x – 3y = -15 y = 3x + 5 9x – 3(3x + 5) = -15 9x -9x - 15 = -15 0x – 15 = -15 - 15 = -15 Many Solutions

Solving Systems with Substitution No Solutions Many Solutions One Solution

Open the foldable so that you can write on the many solution page No Solutions Many Solutions One Solution

{ x – 2y = 3 2x -4y = 1 1. Solve an equation for a variable x – 2y = 3 ____________ +2y x = 2y + 3 No Solution Many Solutions One Solution

x = 2y + 3 x = 2y + 3 2x -4y = 1 2. Substitute eq 3. Answer No Solution When graphed, the lines will never pass 2(2y + 3) – 4y = 1 4y + 6 - 4y = 1 The lines are parallel 0y + 6 = 1 6 = 1 No Solution Many Solutions One Solution

{ Guided Practice 3 Find the solution to the system by substitution: y = 2x -2x + y = 4 { -2x + y = 0 -2x + y = 4 -2x + 1(2x) = 4 -2x + 2x = 4 -2x + y = 0 +2x +2x 0 = 4 ______________ y = 2x No Solution