PSAT Math Multiple-Choice Practice Test 31: The Heart of Algebra: Systems of Linear Equations

1.

If q is a constant and the above system of equations has infinitely many solutions, what is the value of q ?

B.

C.

2.

In the system of linear equations shown above, z is a constant. If the system has no solution, what is the value of z ?

A.

B.

3.

For which of the following values of w will the system of equations above have no solution?

4.

If the system of linear equations shown above has infinitely many solutions, and c is a constant, what is the value of c ?

A.

B.

5. What is the value of x if 25x - 7y = 28 and 10x + 7y + 18 = 60?

A.

B.

D.

6. What is the value of y - x, if 6x - 4y = 8 and 5y - 7x = 12?

7. A bed costs $40 less than three times the cost of a couch. If the bed and couch together cost $700, how much more does the bed cost than the couch?

8.

If k is a constant and the above system of linear equations has infinitely many solutions, what is the value of k?

9.

What is the value of |a - b| if a and b are constants and the above system of equations has no solution?

10. A local airport has separate fees for commercial airliners and private planes. Commercial flights are charged a landing fee of $281 per flight and private planes are charged a landing fee of $31 per flight. On a given day, a total of 312 planes landed at the airport and $47,848 in landing fees was collected. Solving which of the following systems of equations yields the number of commercial airliners, c, and the number of private planes, p, that landed at the airport on the day in question?

A.

B.

C.

D.

11. At a certain coffee store, the small bag of beans costs $2.50 and the large bag of beans costs $15. If the store sold 27 small and large bags of beans and had $155 in revenue in one week, how many small bags and large bags of beans were sold?

12.

If (x, y) is a solution to the system of equations shown above, then what is the value of x - y ?

A.

B.

C.

D.

13. Guests at a wedding had two meal choices, chicken and vegetarian. The catering company charges $12.75 for each chicken dish and $9.50 for each vegetarian dish. If 62 people attended the wedding and the catering bill was $725.25, which of the following systems of equations could be used to find the number of people who ordered chicken, c, and the number of people who ordered vegetarian, v, assuming everyone ordered a meal?

A.

B.

C.

D.

14. Two turkey burgers and a bottle of water cost $3.25. If three turkey burgers and a bottle of water cost $4.50, what is the cost of two bottles of water?