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Applying Systems of Equations – Part 2

Applying Systems of Equations – Part 2. Honors Math – Grade 8. Distribute on both sides of =. 1. Seven times a number plus three times another number is negative one. The sum of the two numbers equals negative three. What are the numbers?. Define the Variables.

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Applying Systems of Equations – Part 2

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  1. Applying Systems of Equations – Part 2 Honors Math – Grade 8

  2. Distribute on both sides of = 1 Seven times a number plus three times another number is negative one. The sum of the two numbers equals negative three. What are the numbers? Define the Variables Let x = the first number and y = the second number. Write a system of equations. Seven times a number plus three times another is -1. 7x + 3y = -1 The sum of the two numbers is -3. x + y = -3 1. Write the equations in column form. Multiply to eliminate a variable. The numbers are 2 and -5.

  3. 2 Mariah invested $25,000 in two mutual funds. One of the funds rose 5% in one year, and the other rose 9% in one year. If Mariah’s investment gained a total of $1770 in one year, how much did she invest in each mutual fund? Define the Variables Let a = the first mutual fund & b = the second mutual fund Write a system of equations. The total investment is 25000. a + b = 25000 The interest gained is 1640. .05a + .09b = 1770 I = prt 1. Write the equations in column form. Multiply to eliminate a variable. Solve the equation Mariah invested $12,000 @ 5% and $13,000 @ 9%.

  4. Distribute 3 The cost of four notebooks and five pens is $20. The cost of six notebooks and two pens is $19. How much does each notebook and pen cost? Define the Variables Let n = the cost of a notebook and p = the cost of a pen. Write a system of equations. 4 notebooks and 5 pens = 20 4n + 5p = 20 6 notebooks and 2 pens = 19. 6n + 2p = 19 1. Write the equations in column form. Multiply to eliminate a variable. Solve the equation 2. Since the coefficients of n are 12 & 12 (the same), subtract the equations. 3. Now substitute p = 2 in either equation and solve. A pen costs $2 and a notebook costs $2.50.

  5. Distribute 4 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. Define the Variables Let b = the rate of the barge in still water and c = the rate of the current. 1. Write the equations in column form; multiply. Write a system of equations. 2. Since the coefficients of c are opposites, ADD the equations. Solve the equation The c variable is eliminated because -6 + 6 = 0 The rate of the barge in still water is 10 miles per hour.

  6. Distribute 5 A canoe travels 4 miles upstream in one hour. The return trip takes the canoe 1.5 hours. Find the rate of the canoe in still water. Define the Variables Let b = the rate of the canoe in still water and c = the rate of the current. 1. Write the equations in column form; multiply. Write a system of equations. 2. Since the coefficients of c are opposites, ADD the equations. Solve the equation The c variable is eliminated because -1.5 + 1.5 = 0 The rate of the canoe in still water is 10/3 miles per hour.

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