PSAT questions-Systems of Linear Equations1

What is the solution (x, y) to the given system of equations? y = 2x + 3 x = 1

• (1,2)

• (1,5)

• (2,3)

• (2,7)

In the xy-plane, the graph of y = x + 3 intersects the graph of y = 2x - 6 at the point (a, b). What is the value of a?

• 3

• 6

• 9

• 12

Which of the following points (x, y) is the solution to the given system of equations in the xy-plane? x = 5 y = x - 8

• (0, 0)

• (5, -3)

• (5, -8)

• (5, 8)

x = 10, y = x + 21. The solution to the given system of equations is (x, y). What is the value of y?

• 2.1

• 10

• 21

• 31

A petting zoo sells two types of tickets. The standard ticket, for admission only, costs $5. The premium ticket, which includes admission and food to give to the animals, costs $12. One Saturday, the petting zoo sold a total of 250 tickets and collected a total of $2,300 from ticket sales. Which of the following systems of equations can be used to find the number of standard tickets, s, and premium tickets, p, sold on that Saturday?

• s + p = 250

• 5s + 12p = 250

• 12s + 5p = 2,300

• 5s + 12p = 2,300

• s + p = 250

Which of the following graphs in the xy-plane could be used to solve the system of equations below? x + 5y = 5 2x - y = -4

• A

• B

• C

• D

-12x + 14y = 36 and -6x + 7y = -18. How many solutions does the given system of equations have?

• Exactly one

• Exactly two

• Infinitely many

• Zero

At how many points do the graphs of the given equations intersect in the xy-plane? y = 2x + 10 and y = 2x - 1

• Zero

• Exactly one

• Exactly two

• Infinitely many

Angela is playing a video game. In this game, players can score points only by collecting coins and stars. Each coin is worth c points, and each star is worth s points. The first time she played, Angela scored 700 points. She collected 20 coins and 10 stars. The second time she played, Angela scored 850 points. She collected 25 coins and 12 stars. Which system of equations can be used to correctly determine the values of c and s?

• 10c + 20s = 700 12c + 25s = 850

• 20c + 10s = 700 25c + 12s = 850

• 20c + 700s = 10 25c + 850s = 12

• 700c + 20s = 10 850c + 25s = 12

The graph of a system of linear equations is shown. What is the solution (x, y) to the system?

• (0, 5)

• (2, 4)

• (5, 10)

• (10, 0)