Solving Systems of Equations By Elimination

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

Warm-Up Solve the system of equations using substitution 1. x + 2y = 6 -x + 2y = - 2 2. y = 2 -2x + 3y = -6

Warm Up 1 Solve the system of equations using substitution 1. x + 2y = 6 -x + 2y = - 2 x + 2y = 6 - 2y - 2y __________ x = -2y + 6 x + 2y = 6 -1(-2y + 6) + 2y = -2 x + 2(1) = 6 2y - 6 + 2y = -2 x + 2 = 6 __________ -2 -2 4y – 6 = -2 x = 4 __________ + 6 + 6 __ 4 __ 4 4y = 4 Solution: (4, 1) y = 1

Warm-Up 2 Solve the system of equations using substitution 2. y = 2 -2x + 3y = -6 -2x + 3(2) = -6 Solution: -2x + 6 = -6 (6, 2) __________ -6 -6 ___ -2 -2x = -12 ___ -2 x = 6

Learning Intention/Success Criteria LI: We are learning how to solve a system of equations by elimination SC: I know how to -determine if a system of equations has many, one, or no solutions -solve systems of two linear equations algebraically using the elimination method -multiply by integers -add and subtract integers

EQ: How Do I Solve a System of Equations by Elimination? 11/29/2018

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Same coefficient, different signs

Same coefficient, different signs Open flap

{ __ 6 Solve by elimination 4x + 5y = 9 -4x + y = 3 2. Substitute value into eq. { 4x + 5y = 9 y = 2 1. Add equations together 4x + 5(2) = 9 4x + 10 = 9 4x + 5y = 9 -4x + y = 3 -10 -10 + + + 4x = -1 __ 4 __ 4 6y = 12 __ 6 __ 6 x = -1/4 y = 2 3. Solution (-1/4, 2)

{ Guided Practice 1 2x + y = 10 x = 4 2(4) + y = 10 8 + y = 10 -8 -8 + Find the solution to the system by elimination: 2x + y = 10 x = 4 2x + y = 10 5x – y = 18 { 2(4) + y = 10 8 + y = 10 2x + y = 10 5x – y = 18 -8 -8 + + + y = 2 7x = 28 __ 7 __ 7 Solution: x = 4 (4, 2)

Same coefficient, different signs Same coefficient, same signs

Same coefficient, different signs Same coefficient, same signs Open flap

{ Solve by elimination 2x + 3y = 2 x + 3y = 7 + + + 3. Substitute value into equation { 2x + 3y = 2 x = -5 1. Multiply one eq. by -1 2(-5) + 3y = 2 2x + 3y = 2 x + 3y = 7 -10 + 3y = 2 -1( ) + 10 + 10 2x + 3y = 2 -x - 3y = -7 3y = 12 __ 3 __ 3 2. Add eqs together y = 4 2x + 3y = 2 -x - 3y = -7 + + + (-5, 4) 4. Solution: x = -5

Guided Practice 2 Find the solution to the system by elimination: -x - 5y = -33 -2x + 5y = -6 + + + { x + 5y = 33 -2x + 5y = -6 -3x = -39 __ -3 __ -3 x = 13 -1 ( ) x + 5y = 33 -2x + 5y = -6 x + 5y = 33 x = 13 13 + 5y = 33 -x - 5y = -33 -2x + 5y = -6 -13 -13 5y = 20 __ 5 __ 5 Solution: (13, 4) y = 4

Same coefficient, different signs Same coefficient, same signs Different coefficients, multiply one equation

Same coefficient, different signs Same coefficient, same signs Different coefficients, multiply one equation Open flap

{ Solve by elimination 3x + y = 7 x + 2y = 34 ___ -5 ___ -5 x = -4 3. Substitute value into equation 1. Multiply eq. by # to make same coefficients -2( ) 3x + y = 7 x = -4 3x + y = 7 x + 2y = 34 3(-4) + y = 7 -12 + y = 7 -6x + -2y = -14 x + 2y = 34 +12 +12 y = 19 2. Add eqs together -6x + -2y = -14 x + 2y = 34 4. Solution + + + (-4, 19) -5x = 20

Guided Practice 3 Find the solution to the system by elimination: x – 2y = 5 y = -1 { x – 2y = 5 4x + 3y = 9 x – 2(-1) = 5 x + 2 = 5 -4( ) x – 2y = 5 4x + 3y = 9 -2 -2 x = 3 -4x + 8y = -20 4x + 3y = 9 + + + Solution: 11y = -11 ___ 11 ___ 11 (3, -1) y = -1

Same coefficient, different signs Same coefficient, same signs Different coefficients, multiply one equation Different coefficients, multiply both equations

Open flap Same coefficient, different signs Same coefficient, same signs Different coefficients, multiply one equation Different coefficients, multiply both equations Open flap

{ Solve by elimination 4x – 3y = 25 -3x + 8y = 10 23y = 115 ___ 23 ___ 23 ___ 23 y = 5 3. Substitute value into equation 1. Multiply eqs. by # to make same coefficients 4x – 3y = 25 y = 5 4x – 3y = 25 -3x + 8y = 10 3( ) 4x – 3(5) = 25 4( ) 4x – 15 = 25 12x + -9y = 75 -12x +32y = 40 +15 +15 4x = 40 ___ 4 ___ 4 2. Add eqs together 12x + -9y = 75 -12x +32y = 40 x = 10 + + + 4. Solution 23y = 115 (10, 5)

{ Guided Practice 4 Find the solution to the system by elimination: 3x – 2y = -5 x = 3 { 8x – 3y = 3 3x – 2y = -5 3(3) – 2y = -5 9 – 2y = -5 -2( ) 8x – 3y = 3 3x – 2y = -5 -9 -9 3( ) – 2y = -14 ___ -2 __ -2 -16x + 6y = -6 9x – 6y = -15 y = 7 -7x = -21 __ -7 __ -7 Solution: (3, 7) x = 3