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.

Number of Solutions and Special Cases Practice — Grade 8 math

Lesson 4: Number of Solutions and Special Cases — 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. A system of two linear equations has no solution. What must be true about the graphs of the two equations?
- A. The lines have different slopes.
- B. The lines have the same slope and the same y-intercept.
- C. The lines have the same slope but different y-intercepts.
- D. The lines are perpendicular.
7. How many solutions does the following system of equations have? $y = 4x - 1$ $y = 4x + 5$ The system has ___ solution(s).
8. How many solutions does the system of equations have? $y = -2x + 3$ $4x + 2y = 6$
- A. No solution
- B. Exactly one solution
- C. Exactly two solutions
- D. Infinite solutions
9. Consider the system of equations: $y = 5x + 2$ $y = -x - 4$ How many solutions does this system have? This system has ___ solution(s).
10. Which term best describes a system of linear equations where the lines have different slopes?
- A. Inconsistent
- B. Consistent and dependent
- C. Consistent and independent
- D. Parallel