Section 5.3: Solving Systems of Linear Equations by Elimination — Practice Questions

1. 1. The sum of two numbers is 37 and their difference is 9. What are the two numbers?

   • A. 23 and 14
   • B. 20 and 17
   • C. 25 and 12
   • D. 19 and 18

2. 2. The sum of two numbers is 65 and their difference is 25. The larger number is ___.

3. 3. The sum of two numbers is -27 and their difference is -59. The smaller number is ___.

4. 4. Two numbers have a sum of -45 and a difference of -89. Find the numbers.

   • A. -67 and 22
   • B. -60 and 15
   • C. -70 and 25
   • D. -65 and 20

5. 5. To solve the system $\begin{cases} 3x + y = 10 \\ 4x - 2y = 2 \end{cases}$ by elimination, what is the first step to eliminate the variable $y$?

   • A. Multiply the first equation by 2.
   • B. Multiply the second equation by -1.
   • C. Add the equations as they are.
   • D. Multiply the first equation by 4 and the second by -3.

6. 6. Solve the system of equations: $\begin{cases} 2x + y = 11 \\ 5x - y = 3 \end{cases}$. The value of $x$ is ___.

7. 7. Solve the system of equations: $\begin{cases} x + 2y = 12 \\ 3x - y = 1 \end{cases}$. The value of $y$ is ___.

8. 8. Consider the system $\begin{cases} 2x + 3y = 3 \\ 5x + 4y = 11 \end{cases}$. Using the elimination method, the value of $y$ is ___.

9. 9. Which of the following describes a correct first step to solve the system $\begin{cases} 4x - 3y = 1 \\ 5x - 2y = 8 \end{cases}$ by elimination?

   • A. Add the two equations together.
   • B. Multiply the first equation by 2 and the second equation by -3.
   • C. Multiply the first equation by 3 and the second equation by 2.
   • D. Multiply the first equation by 5.

10. 10. To solve the system $4x - 3y = 10$ and $2x + 9y = 14$ by elimination, what constant should you multiply the first equation by to eliminate the $y$-variable?

    • A. -3
    • B. 3
    • C. 2
    • D. 9