Multiple Choice

1. If two linear equations are graphed on the same coordinate plane, and they intersect at the point $(3, -2)$, what is the solution to the system of equations?

   $(3, -2)$

   $x=3, y=2$

   $x=-2, y=3$

   $(3, 2)$

2. Solve the system of equations using substitution: $y = 2x - 1$ and $4x + y = 11$.

   $(1, 1)$

   $(3, 2)$

   $(2, 3)$

   $(2, 3)$

3. Solve the system of equations using elimination: $x + y = 7$ and $x - y = 3$.

   $(4, 3)$

   $(5, 2)$

   $(3, 4)$

   $(5, 2)$

4. The sum of two numbers is $15$, and their difference is $3$. What are the two numbers?

   $9$ and $6$

   $8$ and $7$

   $10$ and $5$

   $6$ and $9$

5. Which of the following systems of equations has no solution?

   $y = 3x + 2$ and $y = -3x + 2$

   $y = 2x + 1$ and $2y = 4x + 2$

   $x + y = 5$ and $x - y = 5$

   $y = 2x + 5$ and $y = 2x - 3$

6. Solve the system of equations: $x + 2y = 10$ and $3x - y = 9$.

   $(4, 3)$

   $(4, 3)$

   $(2, 4)$

   $(3, 4)$

7. Solve the system of equations: $2x + y = 11$ and $x - 3y = 9$.

   $(5, 1)$

   $(4, 3)$

   $(6, -1)$

   $(6, -1)$

8. How many solutions does a system of two linear equations have if their graphs are two distinct parallel lines?

   Two solutions

   Infinitely many solutions

   One solution

   No solution

9. A vendor sold $25$ items, consisting of hot dogs and sodas, for a total of $\$70$. If each hot dog costs $\$4$ and each soda costs $\$2$, how many hot dogs were sold?

   $15$

   $20$

   $10$

   $5$

10. Solve the system of equations: $3x + 2y = 13$ and $2x - 3y = 0$.

    $(3, 2)$

    $(3, 2)$

    $(2, 3)$

    $(5, -1)$

11. Which of the following systems of equations has infinitely many solutions?

    $2x + y = 4$ and $4x + 2y = 8$

    $y = 3x - 4$ and $y = -3x - 4$

    $x + y = 1$ and $x + y = 2$

    $2x - y = 5$ and $x + y = 5$

12. What is the $y$-value of the solution to the system: $x = 2y - 5$ and $3x + 4y = 25$?

    $4$

    $3$

    $5$

    $2$

13. John is twice as old as his sister, Mary. In $5$ years, John will be $3$ years older than Mary. How old is Mary now?

    $8$ years old

    $3$ years old

    $10$ years old

    $5$ years old

14. Solve the system: $\frac{1}{2}x + y = 4$ and $x - y = 2$.

    $(4, 2)$

    $(6, 4)$

    $(4, 2)$

    $(2, 3)$

15. For the system of equations $y = mx + b$ and $y = nx + c$, under what conditions will the system have exactly one solution?

    $m \neq n$

    $m = n$ and $b = c$

    $b = c$

    $m = n$ and $b \neq c$

16. A jar contains $20$ coins, all dimes and quarters. The total value of the coins is $\$3.50$. How many quarters are in the jar?

    $10$

    $8$

    $12$

    $5$

17. Solve the system of equations: $5x + 3y = 21$ and $5x - 2y = 11$.

    $(1, 4)$

    $(3, 2)$

    $(2, 3)$

    $(4, 1)$

18. A boat travels $24$ miles downstream in $2$ hours and returns upstream the same distance in $3$ hours. What is the speed of the current in miles per hour?

    $1 \text{ mph}$

    $2 \text{ mph}$

    $4 \text{ mph}$

    $3 \text{ mph}$

19. Solve the system: $y = 3x - 7$ and $5x - 2y = 12$.

    $(3, 2)$

    $(1, -4)$

    $(4, 5)$

    $(2, -1)$

20. Which of the following statements is true for the system $y = 5x + 3$ and $10x - 2y = -6$?

    The system has infinitely many solutions.

    The lines are perpendicular.

    The lines are parallel and distinct.

    The system has exactly one solution.

21. Solve the system: $4x + y = 14$ and $3x - 2y = 5$.

    $(2, 6)$

    $(3, 2)$

    $(4, -2)$

    $(1, 10)$

22. A chemistry student needs to mix a $10\%$ acid solution with a $40\%$ acid solution to obtain $100$ mL of a $25\%$ acid solution. How much of the $10\%$ solution is needed?

    $75 \text{ mL}$

    $40 \text{ mL}$

    $60 \text{ mL}$

    $50 \text{ mL}$

23. Which ordered pair is the solution to the system: $2x - 3y = 7$ and $x + 2y = 0$?

    $(-2, 1)$

    $(5, 1)$

    $(1, -2)$

    $(2, -1)$

24. Solve the system: $\frac{x}{3} + \frac{y}{2} = 2$ and $\frac{x}{6} - \frac{y}{4} = 0$.

    $(3, 2)$

    $(4, 3)$

    $(2, 4)$

    $(1, 1)$

25. A theater sold $400$ tickets for a play. Adult tickets cost $\$15$ and child tickets cost $\$10$. If the total revenue was $\$5000$, how many child tickets were sold?

    $250$

    $200$

    $100$

    $150$