When solving a system of linear equations by elimination, you get the equation $0 = 8$. What does this imply about the system?

The system has exactly one solution.

The system has infinitely many solutions.

The solution is the point $(0, 8)$.

If solving a system of linear equations results in the true statement $0 = 0$, what does this reveal about the graphs of the two equations?

The lines intersect at the origin.

Solve Systems of Equations by Elimination Practice — Grade 8 math

Lesson 6-4: Solve Systems of Equations by Elimination — Practice Questions

1. When solving a system of linear equations by elimination, you get the equation $0 = 8$. What does this imply about the system?
- A. The system has exactly one solution.
- B. The system has no solution.
- C. The system has infinitely many solutions.
- D. The solution is the point $(0, 8)$.
2. Consider the system: $2x - y = 4$ and $-6x + 3y = -10$. After multiplying the first equation by 3 and adding the equations, the result is $0 = \_\_\_$.
3. How many solutions does the system of equations $3x - 9y = 15$ and $-x + 3y = -5$ have?
- A. No solution
- B. One solution
- C. Two solutions
- D. Infinitely many solutions
4. If solving a system of linear equations results in the true statement $0 = 0$, what does this reveal about the graphs of the two equations?
- A. The lines are parallel.
- B. The lines are the same.
- C. The lines are perpendicular.
- D. The lines intersect at the origin.
5. Using elimination on the system $x + 5y = 3$ and $-2x - 10y = -6$, both variables cancel out. The resulting equation is $0 = \_\_\_$.
6. To solve the system of equations $5x - 3y = 7$ and $2x + 3y = 14$ using elimination, which operation should you perform first to eliminate the $y$ variable?
- A. Add the two equations
- B. Subtract the second equation from the first
- C. Multiply the first equation by 3
- D. Divide the second equation by 2
7. When you add the equations $3x - 2y = 8$ and $x + 2y = 12$ to eliminate $y$, the resulting simplified equation is $4x = \_\_\_$.
8. Consider the system: $4a + 5b = 11$ and $a + 5b = 2$. Which is the correct first step to eliminate the variable $b$?
- A. Add the two equations
- B. Subtract the second equation from the first
- C. Multiply the second equation by 4
- D. Add 5 to both sides
9. If you subtract the equation $2m + 3n = 9$ from $5m + 3n = 15$, the resulting simplified equation is $3m = \_\_\_$.
10. If you subtract the second equation from the first in the system below, which variable will be eliminated? System: $7p + 2q = 10$ and $7p - 5q = 3$.
- A. p
- B. q
- C. Both p and q
- D. Neither variable