Deck 7: Section 2: Systems of Linear Equations

Question 1

Solve the system of equations.
3x - 2y + 4z = 12
-5x - y - z = -10
-3x - 5y - 3z = -4

Answer 1

{(2, -1, 1)}

Question 2

Solve by graphing. Label each line and the solution point.

Answer 2

Question 3

Solve the system of linear equations by the substitution method.

Answer 3

Question 4

Fred, Tiger, and Nancy play a round of golf together. Their combined score is 226. Fred's score was 5 more than Tiger's, and Nancy's score was 9 more than Fred's. What was each person's score?

Question 5

Solve the system of linear equations.

Question 6

When rolling a pair of dice, the probability of getting a particular total is not very high. For example, the probability of failing to roll a total of 3 is 17 times the probability of successfully rolling a total of 3. The total probability (probability of failing to roll a 3 + probability of successfully rolling a 3) is 1. What is the probability of rolling a 3?

Question 7

Solve the system of equations.

Question 8

Cashews sell for $5 per pound and peanuts sell for $2 per pound. How many pounds of each would you use to make 15 pounds of a mixture that sells for $3.20 per pound?

Question 9

Solve the system of linear equations by the substitution method.
-5x = -2y + 9
5x + 5y = -30

Question 10

Suzanne invested $14,300 in two mutual fund accounts: the Abernathy Fund and the Brice Fund. During the subsequent year, The Abernathy Fund earned 4% and the Brice account earned 5%. At the end of the year, the total interest earned was $672. How much did Suzanne invest in each fund?

Question 11

Solve the system of equations.
-3.5x + 3y = -5.375
-0.875x - 0.5y = 0.53125

Question 12

For Monday morning's staff meeting, Jim bought 2 bags of bagels and 3 packages of cream cheese and paid $9.00 (excluding sales tax). For Friday's meeting, he bought 4 bags of bagels and 2 packages of cream cheese and paid $10.00 (again, excluding sales tax). How much do bags of bagels and packages of cream cheese cost?

Question 13

For the system find the value of a so that the solution set to the system is {(4, 7)}.

Question 14

Solve the system of equations.
-x + 5y - 3z = 31
-4x - 5y + 4z = 6
3x - 15y + 9z = -91

Question 15

Solve the system of linear equations by the substitution method. Then, state whether the system is independent, dependent, or inconsistent.
4x - 3y = 4
12x - 9y = 12