1. Lesson 7-4 Elimination Using Multiplication

2. Use elimination to solve each system of equations. Ex. 1 3x + 4y = 6 5x + 2y = -4 Multiply one equation to Eliminate

3. Use elimination to solve each system of equations. 2x + y = 23 3x + 2y = 37 Multiply one equation to Eliminate

4. Ex. 2 3x + 4y = -25 2x - 3y = 6 Multiply Both Sides to Eliminate

5. 4x + 3y = 8 3x - 5y = -23 Multiply Both Sides to Eliminate

6. MethodThe Best Time to Use GraphingTo estimate the solution, since graphing usually does not give an exact solution SubstitutionIf 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.

7. Determine the best method to solve the system of equations. Then solve the system. Ex. 3 4x - 3y = 12 x + 2y = 14 Determine the Best Method

8. Determine the best method to solve the system of equations. Then solve the system. x + 5y = 4 3x - 7y = -10 Determine the Best Method

9. 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 Equations Ex 4 rtdr t = d Downstreamb + c2242b + 2c = 24 Upstreamb - c3243b - 3c = 24 Let b = the rate of the barge and c = the rate of the current.

10. 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 Equations Ex 4 2b + 2c = 24 3b - 3c = 24

11. 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 rtdr t = d Downstreamb + c1/2101/2b + 1/2c = 10 Upstreamb - c2/3102/3b - 2/3c = 10 Let b = the rate of the boat and c = the rate of the current.

12. 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 = 10 2/3b - 2/3c = 10