Multiple Choice

1. Two numbers have a sum of $25$ and a difference of $7$. Let the numbers be $x$ and $y$. The system of equations is:

   $16$ and $9$

   $18$ and $7$

   $17$ and $8$

   $15$ and $10$

2. A total of $18$ students are in a classroom. There are twice as many girls as boys. Let $g$ be the number of girls and $b$ be the number of boys. The system of equations is:

   $8$ girls

   $12$ girls

   $6$ girls

   $10$ girls

3. Solve the system using elimination: $2x + 3y = 12$; $3x - 2y = 5$.

   $x = 3, y = -2$

   $x = 3, y = 2$

   $x = 0, y = 4$

   $x = 2, y = 3$

4. Solve the system using elimination: $x - 2y = 6$; $-2x - y = -7$.

   $x = 4, y = -1$

   $x = 2, y = -2$

   $x = -4, y = -1$

   $x = 4, y = 1$

5. Solve the system using elimination: $3x + y = -1$; $x - 3y = -17$.

   $x = 1, y = -4$

   $x = -2, y = 5$

   $x = 2, y = 5$

   $x = -2, y = -5$

6. Solve the system using elimination: $y = 7$; $x = 0$.

   $x = 0, y = 7$

   $x = 0, y = 0$

   $x = 7, y = 7$

   $x = 7, y = 0$

7. Solve the system using elimination: $x = 5$; $-y = 0$.

   $x = 5, y = 0$

   $x = 5, y = 1$

   $x = -5, y = 0$

   $x = 0, y = 5$

8. Solve the system using elimination: $4x + 5y = -32$; $5x - 4y = 1$.

   $x = 1, y = -8$

   $x = -3, y = -4$

   $x = 3, y = -4$

   $x = -3, y = 4$

9. Solve the system using elimination: $x + 2y = 12$; $2x - 3y = 0$.

   $x = 6, y = 3$

   $x = 6, y = -3$

   $x = -6, y = 3$

   $x = 4, y = 4$

10. Solve the system using elimination: $2x + y = 13$; $x - 2y = -16$.

    $x = 3, y = 7$

    $x = -2, y = 9$

    $x = 2, y = 9$

    $x = 2, y = -9$

11. Solve the system using elimination: $3x - y = -16$; $-x - 3y = 2$.

    $x = -5, y = -1$

    $x = -5, y = 1$

    $x = 5, y = 1$

    $x = -4, y = 4$

12. Solve the system using elimination: $5x + 2y = 31$; $2x - 5y = 24$.

    $x = -7, y = -2$

    $x = 7, y = 2$

    $x = 5, y = 3$

    $x = 7, y = -2$

13. Solve the system using elimination: $x + y = 2$; $x - y = 0$.

    $x = -1, y = 3$

    $x = 2, y = 0$

    $x = 1, y = 1$

    $x = 0, y = 2$

14. Solve the system using elimination: $2x = 16$; $-2y = -8$.

    $x = 8, y = 4$

    $x = 4, y = 8$

    $x = -8, y = 4$

    $x = 8, y = -4$

15. Solve the system using elimination: $3y = -18$; $3x = 9$.

    $x = -3, y = -6$

    $x = -6, y = 3$

    $x = 3, y = -6$

    $x = 3, y = 6$

16. Solve the system using elimination: $x - 3y = -13$; $-3x - y = 19$.

    $x = -7, y = 2$

    $x = 7, y = 2$

    $x = -7, y = -2$

    $x = -1, y = 4$

17. Solve the system using elimination: $2x - y = 23$; $-x - 2y = -4$.

    $x = 10, y = 3$

    $x = 10, y = -3$

    $x = 8, y = -7$

    $x = -10, y = -3$

18. Solve the system using elimination: $3x + 2y = 24$; $2x - 3y = -10$.

    $x = 2, y = 9$

    $x = 4, y = -6$

    $x = -4, y = 6$

    $x = 4, y = 6$

19. Solve the system using elimination: $4x + y = -16$; $x - 4y = 30$.

    $x = 2, y = -8$

    $x = -2, y = 8$

    $x = 0, y = -16$

    $x = -2, y = -8$

20. Solve the system using elimination: $x = 9$; $-y = 0$.

    $x = 9, y = 0$

    $x = 0, y = 9$

    $x = 9, y = 1$

    $x = -9, y = 0$

21. Solve the system using elimination: $2x + 3y = 6$; $4x + 6y = 10$.

    $x = 3, y = 0$

    $x = 0, y = 2$

    Infinitely many solutions

    No solution

22. Solve the system using elimination: $3x - 2y = 7$; $6x - 4y = 14$.

    $x = 0, y = 0$

    Infinitely many solutions

    No solution

    $x = 1, y = 0$

23. At the cinema, adult tickets cost $12 and child tickets cost $8. If 16 tickets were sold for a total of $148, how many adult tickets and how many child tickets were sold?

    11 adult tickets and 5 child tickets

    6 adult tickets and 10 child tickets

    4 adult tickets and 12 child tickets

    5 adult tickets and 11 child tickets

24. A shop sells packs of pens for $2 each and pencils for $1 each. A student buys 17 items and spends $23. How many pen packs and how many pencils did the student buy?

    11 pen packs and 6 pencils

    6 pen packs and 11 pencils

    5 pen packs and 12 pencils

    7 pen packs and 10 pencils

25. Two siblings' ages add to 26. The older is 4 years older than the younger. What are their ages?

    Older: 11, Younger: 15

    Older: 15, Younger: 11

    Older: 14, Younger: 12

    Older: 16, Younger: 10

26. A fruit seller has apples and oranges. There are 17 pieces in total. Each apple weighs 150 grams and each orange weighs 200 grams. The total weight is 2800 grams. How many apples and how many oranges are there?

    10 apples and 7 oranges

    13 apples and 4 oranges

    12 apples and 5 oranges

    5 apples and 12 oranges

27. On a farm there are chickens and cows. Together they have 20 heads and 56 legs. How many chickens and how many cows are there?

    14 chickens and 6 cows

    10 chickens and 10 cows

    12 chickens and 8 cows

    8 chickens and 12 cows

28. A coin jar has only quarters (25¢) and dimes (10¢). There are 26 coins totaling $4.10. How many quarters and how many dimes are there?

    16 quarters and 10 dimes

    8 quarters and 18 dimes

    10 quarters and 16 dimes

    12 quarters and 14 dimes

29. At a school fair, shirts cost $15 and hats cost $5. A stall sold 18 items and made $170. How many shirts and how many hats were sold?

    10 shirts and 8 hats

    8 shirts and 10 hats

    9 shirts and 9 hats

    7 shirts and 11 hats

30. The sum of two whole numbers is 35, and their difference is 7 (larger minus smaller). What are the two numbers?

    Larger: 20, Smaller: 15

    Larger: 22, Smaller: 13

    Larger: 14, Smaller: 21

    Larger: 21, Smaller: 14

31. A class orders pencils and erasers. Pencils cost $3 and erasers cost $2. They buy 29 items and spend $76. How many pencils and how many erasers did they buy?

    18 pencils and 11 erasers

    17 pencils and 12 erasers

    11 pencils and 18 erasers

    19 pencils and 10 erasers

32. A commuter center sells bus passes for $30 and train passes for $45. In one day they sell 23 passes and collect $870. How many bus passes and how many train passes were sold?

    13 bus passes and 10 train passes

    11 bus passes and 12 train passes

    10 bus passes and 13 train passes

    12 bus passes and 11 train passes