Lesson 63: Solving Systems of Linear Equations by Elimination — Practice Questions

1. 1. To solve the system below by eliminating the $y$ variable, what is the best first step? $ \begin{cases} 4x - 3y = 8 \\ 2x + 9y = 10 \end{cases} $

   • A. Multiply the first equation by 3.
   • B. Multiply the second equation by 3.
   • C. Add the equations together as they are.
   • D. Multiply the first equation by -3.

2. 2. To prepare the system $4x - y = 9$ and $5x + 3y = 1$ for elimination of the $y$ variable, the first equation is multiplied by 3. The new first equation is ___.

3. 3. Solve the system of equations using elimination: $3x + 2y = 7$ and $2x - 5y = -8$. The value of $x$ is ___.

4. 4. Which set of operations will prepare the system below for eliminating the $x$ variable? $ \begin{cases} 5x + 2y = 7 \\ 3x + 5y = 1 \end{cases} $

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

5. 5. Solve the system of equations: $5x - 2y = 24$ and $3x + y = 10$. What is the value of $y$? The value of $y$ is ___.

6. 6. Consider the system of equations: $4x + 2y = 14$ and $-4x + 5y = 7$. If you add the equations to eliminate $x$, what is the value of $y$? ___

7. 7. For elimination by addition to work, what must be true about the coefficients of the variable you want to eliminate in the two equations?

   • A. The coefficients must be the same.
   • B. The coefficients must be opposites.
   • C. The coefficients must both be 1.
   • D. The coefficients must be negative.

8. 8. Solve the following system for the variable $b$: $7a - 6b = 3$ and $-7a - 4b = 17$. The value of $b$ is ___.

9. 9. What is the solution $(x, y)$ to the system of equations: $x + 6y = 20$ and $-x + 2y = 4$?

   • A. (2, 3)
   • B. (3, 2)
   • C. (-2, 3)
   • D. (2, -3)

10. 10. When adding the equations $6x + 3y = 5$ and $-6x + 2y = 10$ to eliminate $x$, the resulting simplified equation is $5y = \_\_\_$.