PSAT Math Multiple-Choice Practice Test 30: The Heart of Algebra: Systems of Linear Equations


What is the value of x for the given equations above?

2. A television set costs $25 less than twice the cost of a radio. If the television and radio together cost $200, how much more does the television cost than the radio?

3. At a snack stand, hot dogs cost $3.50 and hamburgers cost $5.00. If the snack stand sold 27 snacks and made $118.50 in revenue, how many hot dogs and how many hamburgers were sold?

4. A certain student cell phone plan charges $0.10 per text and $0.15 per picture, with no additional monthly fee. If a student sends a total of 75 texts and pictures in one month and is billed $8.90 for that month, how many more texts did he send than pictures?


In the system of linear equations shown, z represents a constant. If the system of equations has infinitely many solutions, what is the value of z ?

6. Clarice had twice as many nickels as dimes in her piggy bank. When she adds 4 more nickels, she has three times as many nickels as dimes. What was the total number of nickels and dimes in Clarice's piggy bank before she added the additional nickels?


What is the value of x - y from the solution of the above system of equations?

8. If 3r + 2s = 24 and r + s = 12, what is the value of r + 6?

9. At a certain restaurant, there are 25 tables and each table has either 2 or 4 chairs. If a total of 86 chairs accompany the 25 tables, how many tables have exactly 4 chairs?


What is the y-coordinate of the solution to the system of equations shown?

11. If -8c - 3b = 11 and 6b + 6c = 4, what is the value of 3b - 2c ?

12. If 6a + 6b = 30 and 3a + 2b = 14, then what are the values of a and b ?

13. Sixty people attended a concert. Children's tickets sold for $8 each and adult tickets sold for $12 each. If $624 was collected in ticket money, how many more adults than children attended the concert?


What is the value of if the (x, y) solution of the above system of equations is (-5, 2)?

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