To solve the system $4x - y = 11$ and $2x + 3y = 21$ using elimination, which action would be a correct first step to eliminate the $y$ variable?

Multiply the first equation by 3.

Multiply the second equation by 2.

Add the two equations together as they are.

Subtract the second equation from the first.

Systems of Linear Equations Practice — Grade 8 math

Lesson 3: Systems of Linear Equations — Practice Questions

1. Solve the system of equations: $a + b = 15$ and $a - b = 7$. What is the value of $a$? ___
2. Solve the system of equations: $5x + 2y = 21$ and $3x + 2y = 15$. What is the solution $(x, y)$?
- A. (3, 3)
- B. (9, -12)
- C. (1, 8)
- D. (5, -2)
3. Consider the system $3x + 2y = 16$ and $x + y = 7$. By using the elimination method, what is the value of $y$? ___
4. Use the substitution method to solve the system of equations: $y = 2x$ and $5x + 3y = 33$. What is the solution $(x, y)$?
- A. (3, 6)
- B. (6, 3)
- C. (11, 22)
- D. (2, 4)
5. To solve the system $4x - y = 11$ and $2x + 3y = 21$ using elimination, which action would be a correct first step to eliminate the $y$ variable?
- A. Multiply the first equation by 3.
- B. Multiply the second equation by 2.
- C. Add the two equations together as they are.
- D. Subtract the second equation from the first.
6. Which ordered pair is a solution to the system of equations $$\begin{cases} x - 2y = 6 \\ 3x + y = 4 \end{cases}$$?
- A. (4, -1)
- B. (0, -3)
- C. (2, -2)
- D. (1, 1)
7. The ordered pair $(3, b)$ is a solution to the system of equations $$\begin{cases} x + y = 5 \\ 2x - y = 4 \end{cases}$$. What is the value of $b$? ___
8. Is the ordered pair $(4, -1)$ a solution to the system of equations $$\begin{cases} 2x + y = 7 \\ x - y = -1 \end{cases}$$?
- A. No, because it does not satisfy the second equation.
- B. No, because it does not satisfy the first equation.
- C. Yes, because it satisfies the first equation.
- D. Yes, because it satisfies both equations.
9. The ordered pair $(1, 5)$ is tested as a solution for the system $$\begin{cases} y = 3x + 2 \\ y = -2x + 7 \end{cases}$$. It satisfies the first equation. When substituted into the second equation, $y$ evaluates to ___.
10. Why is the ordered pair $(1, 1)$ not a solution to the system of equations $$\begin{cases} 4x - y = 3 \\ x + y = 1 \end{cases}$$?
- A. It does not satisfy the equation $4x - y = 3$.
- B. It does not satisfy the equation $x + y = 1$.
- C. It does not satisfy either equation.
- D. A solution must contain a zero.