Exam 9: Systems of Equations

Solve the problem. -A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 9% cement should he mix with 10 bags of 10.8% cement to produce a mix containing 10% cement?

Solve the system of equations by the elimination method. -0.3x + 0.5y = 3.1 x - 0.1y = 1.5

Solve. -The largest angle of a triangle is 6 times the smallest angle and it is 3 times the other angle. Find the measure of the smallest angle.

Solve the system of equations by the elimination method. -x + 3y = 15 -6x + 4y = 20

Solve. -In triangle ABC, the measure of angle B is 5° more than three times the measure of angle A. The measure of angle C is 15° more than the measure of angle A. Which one of the following is true?

Solve by the substitution method. -8x + 8y = -32 5x - 4y = -20

Solve by the substitution method. -6x + 9y = 114 4x - 4y = -4

Solve graphically. -2x + y = -2 2x + 2y = 4

Solve the problem using the elimination method. -A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $5.00. Another customer buys 4 hot dogs and 3 bags of potato chips for $9.00. Find the cost of each item.

Solve. -Jane wants to buy a photocopier. The salesperson has the following information on 3 models. If all 3 are used, a specific job can be done in 50 minutes. If copier A operates for 20 minutes and copier B for 50 minutes, one-half The job is finished. If copier B operates for 30 minutes and copier C for 80 minutes, three-fifths of the job is done. Which is the fastest copier, and how long does it take for this copier to finish the whole job?

Solve graphically. -3x - 2y = 4 -6x + 4y = 7

Solve by the substitution method. -7x + 9y = -54 -3x - 4y = 24

Solve. -5x + 2y + z = -11 2x - 3y - z = 17 7x + y + 2z = -4

Solve the problem using the elimination method. -In a basketball game, Will scored 40 points, consisting only of three-point shots and two-point shots. He made a total of 17 shots. How many shots of each type did he make?

Solve by the substitution method. -x + y = -1 x + y = 4

Solve the problem using the elimination method. -In a right triangle, one acute angle is 54° more than twice the other. Find each acute angle.

Solve. -x - y + z = -8 x + y + z = -10 X + y - z = 0

Classify the system as consistent or inconsistent, and dependent or independent. --10x - 2y = 10 5x - y = -5

Solve using the substitution method. -y = 2x - 4 4x + y = -28

Solve. -x - y + 5z = -23 5x + z = -5 X + 2y + z = -9