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

**1.**

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?

**5.**

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?

**7.**

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

**8.** If 3*r* + 2*s* = 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?

**10.**

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

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

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

*a*= 2;

*b*= 2

*a*= 4;

*b*= 1

*a*= 1;

*b*= 4

*a*= 3;

*b*= 1

**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?

**14.**

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

### Test Information

- 14 questions
- 20 minutes
- See All test questions

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