Lesson 6-3 – Solving Systems Using Elimination

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Presentation transcript:

Lesson 6-3 – Solving Systems Using Elimination Agenda Lesson 6-3 – Solving Systems Using Elimination Standards 9.0 Solve a system of two linear equations in two variables algebraically. Warm Up Review Notes – Elimination Practice Homework – Page 576 problems 7 to 12 all

Homework – Page 576 problems 7 to 12 all Warm Up Solve each system using substitution y = 4x – 2 y = 2x + 4 b. y = 2x + 10 y = –3x 2x + 3y = 22 9x – 3y = 0 Homework – Page 576 problems 7 to 12 all

Substitution Method Elimination Method – add or subtract two equations to eliminate one variable Example – add: 3x + 2y = 14 2x – 2y = 11 to get: 5x = 25 and eliminate y to get x = 5

1 EXAMPLE Adding Equations Solve by using elimination: 5x – 6y = –32 Page 287 5x – 6y = –32 3x + 6y = 48 Solve by using elimination: Step 1: Eliminate y because the sum of the coefficients of y is 0 5x – 6y = –32 3x + 6y = 48 Step 2: Solve for the other variable in either equation 3x + 2y = 48 Check: Does 5(2) – 6(7) = –32? Yes so (2, 7) is the solution

Multiplying one equation EXAMPLE 3 Multiplying one equation Page 288 2x + 5y = –22 10x + 3y = 22 Solve by using elimination: Step 1: Eliminate one variable 2x + 5y = –22 10x + 3y = 22 5(2x + 5y = –22) 10x + 3y = 22 10x + 25y = –110 10x + 3y = 22 Step 2: solve for the remaining variable 22y = –132 Step 3: solve for the eliminated variable 2x + 5(–6) = –22 Solution is (4, –6)

Homework – Please do at home tonight Class work – Please do these now Page 290/291 problems 1 to 6 and 9 to 11 all Homework – Please do at home tonight Page 576 problems 7 to 12 all

Lesson 6-3 – Solving Systems Using Elimination Agenda Lesson 6-3 – Solving Systems Using Elimination Standards 9.0 Solve a system of two linear equations in two variables algebraically. Warm Up Review Notes – Elimination Practice Homework – Finish Worksheet 6–3

Homework – Finish Worksheet 6–3 Warm Up Solve each system using elimination y = 4x – 2 y = 3x + 4 b. y = 2x + 10 y = 3x 2x + 4y = 22 8x – 4y = 8 Homework – Finish Worksheet 6–3

Multiplying both equations EXAMPLE 5 Multiplying both equations Page 290 4x + 2y = 14 7x – 3y = –8 Solve by using substitution: Step 1: Eliminate one variable 4x + 2y = 14 7x – 3y = –8 3(4x + 2y = 14) 2(7x – 3y = –8) 12x + 6y = 42 14x – 6y = –16 Step 2: solve for the remaining variable 26x = 26 Step 3: solve for the eliminated variable 4(1) + 2y = 14 Solution is (1, 5)

Multiplying both equations EXAMPLE 5a Multiplying both equations 3x + 5y = 19 2x – 4y = –2 Solve by using substitution: Step 1: Eliminate one variable 3x + 5y = 19 2x – 4y = –2 2(2x + 5y = 19) 3(3x – 4y = –2) 6x + 10y = 38 6x – 12y = –6 Step 2: solve for the remaining variable 22y = 44 Step 3: solve for the eliminated variable 3x + 5(2) = 19 Solution is (3, 2)

Homework – Please do at home tonight Class work – Please do these now Page 291 problems 17 to 22 all and 24 to 28 even Homework – Please do at home tonight Finish Worksheet 6–3