A system of equations is defined by $y = -2x + 5$ and $4x + 2y = 10$. What does this system represent geometrically?

Two distinct intersecting lines

Solving and Classifying Special Systems of Linear Equations Practice — Grade 9 math

Lesson 67: Solving and Classifying Special Systems of Linear Equations — Practice Questions

1. When solving a system of equations, an algebra student simplifies the system to the statement $5 = 5$. How many solutions does this system have?
- A. No solution
- B. Exactly one solution
- C. Exactly two solutions
- D. Infinitely many solutions
2. If you solve the system $2x - 5y = 10$ and $4x - 10y = 20$ using the elimination method, the variables cancel out, leaving the equation $0 = \_\_\_$.
3. How would you classify the system of equations given by $4x + y = 3$ and $12x + 3y = 9$?
- A. Inconsistent
- B. Dependent
- C. Consistent and independent
- D. Non-linear
4. To solve the system $y = 2x - 1$ and $6x - 3y = 3$, you substitute the expression for $y$ from the first equation into the second. After simplifying, this results in the true statement $3 = \_\_\_$.
5. A system of equations is defined by $y = -2x + 5$ and $4x + 2y = 10$. What does this system represent geometrically?
- A. Two distinct intersecting lines
- B. Two parallel lines
- C. A single line
- D. Two perpendicular lines
6. A system of linear equations is described as consistent and independent. How many solutions does this system have?
- A. No solution
- B. Exactly one solution
- C. Exactly two solutions
- D. Infinitely many solutions
7. What is the value of $x$ in the solution to the system of equations: $y = 3x + 2$ and $y = -x + 10$? The value of $x$ is ___.
8. What is the value of $y$ in the solution to the system of equations: $y = 4x - 5$ and $y = 2x + 1$? The value of $y$ is ___.
9. What is the solution $(x, y)$ to the system of equations $y = 5x - 1$ and $y = 3x + 5$?
- A. (3, 14)
- B. (2, 9)
- C. (3, 4)
- D. (14, 3)
10. Which statement correctly describes the system of equations $y = -2x + 8$ and $y = x + 2$?
- A. It is consistent and independent because it has a unique solution at (2, 4).
- B. It is inconsistent because the lines are parallel.
- C. It is dependent because the lines are the same.
- D. It is consistent and independent because it has a unique solution at (3, 5).