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Lesson 7-4 Elimination Using Multiplication

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Page 1: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

Lesson 7-4

Elimination Using Multiplication

Page 2: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

Use elimination to solve each system of equations.

Ex. 1

3x + 4y = 65x + 2y = -4

Multiply one equation to Eliminate

Page 3: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

Use elimination to solve each system of equations.

2x + y = 233x + 2y = 37

Multiply one equation to Eliminate

Page 4: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

Ex. 2

3x + 4y = -252x - 3y = 6

Multiply Both Sides to Eliminate

Page 5: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

4x + 3y = 83x - 5y = -23

Multiply Both Sides to Eliminate

Page 6: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

Method The Best Time to Use

Graphing To estimate the solution, since graphing usually does not give an exact solution

Substitution If one of the variables in either equation has a coefficient of 1 or -1.

Elimination Using Addition

If one of the variables has opposite coefficients in the two equations.

Elimination Using Subtraction

If one of the variables has the same coefficient in the two equations.

Elimination Using Multiplication

If none of the coefficients are 1 or -1 and neither of the variables can be eliminated by simply adding or subtracting the equations.

Page 7: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

Determine the best method to solve the system of equations. Then solve the system.

Ex. 3

4x - 3y = 12x + 2y = 14

Determine the Best Method

Page 8: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

Determine the best method to solve the system of equations. Then solve the system.

x + 5y = 43x - 7y = -10

Determine the Best Method

Page 9: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

A coal barge on the Ohio River travels 24 miles upstream in 3 hours. The return trip takes the barge only 2 hours. Find the rate of the barge in still water.

Write and Solve a System of EquationsEx 4

r t d r t = d

Downstream b + c 2 24 2b + 2c = 24

Upstream b - c 3 24 3b - 3c = 24

Let b = the rate of the barge and c = the rate of the current.

Page 10: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

A coal barge on the Ohio River travels 24 miles upstream in 3 hours. The return trip takes the barge only 2 hours. Find the rate of the barge in still water.

Write and Solve a System of EquationsEx 4

2b + 2c = 243b - 3c = 24

Page 11: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

A fishing boat travels 10 miles down stream in 30 minutes. The return trip takes the boat 40 minutes. Find the rate of the boat in still water.

Write and Solve a System of Equations

r t d r t = d

Downstream b + c 1/2 10 1/2b + 1/2c = 10

Upstream b - c 2/3 10 2/3b - 2/3c = 10

Let b = the rate of the boat and c = the rate of the current.

Page 12: Lesson 7-4 Elimination Using Multiplication. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to

A fishing boat travels 10 miles down stream in 30 minutes. The return trip takes the boat 40 minutes. Find the rate of the boat in still water.

Write and Solve a System of Equations

1/2b + 1/2c = 102/3b - 2/3c = 10

Write the least common multiple. 3. 4. 5. - USD 475 Geary ... · Holt Algebra 1 6-3 Solving Systems by Elimination Warm Up Simplify each expression. 1. 2y – 4x – 2(4y – 2x)

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2x 4y 10 2 x + 4y 2x + 4y = 102 x + 4y + 102= 180 2x = 102 - 4y 51 – 2y + 4y + 102 = 180 2y + 153 = 180 2y = 27 x = 51 - 2y x = 51 – 2(13.5) x = 51 – 27

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Can I use elimination to solve this system of equations? 2x + y = 23 3x + 2y = 37