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

2. The numbers are 2 and -5. 1. Write the equations in column form. Multiply to eliminate a variable. 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? 1 Let x = the first number and y = the second number. Define the Variables 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 Distribute on both sides of =

3. Mariah invested $12,000 @ 5% and $13,000 @ 9%. 1. Write the equations in column form. Multiply to eliminate a variable. 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? 2 Let a = the first mutual fund & b = the second mutual fund Define the Variables Write a system of equations. The total investment is 25000. a + b = 25000 The interest gained is 1640..05a +.09b = 1770 I = prt Solve the equation

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

5. rtdd=rt Downb + c224 2(b + c) = 24 Upb – c324 3(b – c) = 24 The rate of the barge in still water is 10 miles per hour. The c variable is eliminated because -6 + 6 = 0 Solve the equation 1. Write the equations in column form; multiply. 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. 4 Let b = the rate of the barge in still water and c = the rate of the current. Define the Variables Write a system of equations. Distribute 2. Since the coefficients of c are opposites, ADD the equations.

6. rtdd=rt Downb - c1.54 1.5(b + c) =4 Upb + c14 1(b – c) = 4 The rate of the canoe in still water is 10/3 miles per hour. The c variable is eliminated because -1.5 + 1.5 = 0 Solve the equation 1. Write the equations in column form; multiply. 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. 5 Let b = the rate of the canoe in still water and c = the rate of the current. Define the Variables Write a system of equations. Distribute 2. Since the coefficients of c are opposites, ADD the equations.