When solving a system by elimination and both variables cancel, leaving $0 = 7$, what does this tell you about the system?

The system has exactly one solution

The system has infinitely many solutions

The system needs a different method

When both variables are eliminated during elimination by multiplication and the result is a true statement, what geometric relationship do the two lines have?

They are perpendicular and intersect once

They are parallel and never intersect

They are the same line and overlap completely

They intersect at the origin only

6-4 Elimination Using Multiplication Practice — Grade 9 math

6-4 Elimination Using Multiplication — Practice Questions

1. When solving a system by elimination and both variables cancel, leaving $0 = 7$, what does this tell you 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 system needs a different method
2. Solve the system $3x + 4y = 10$ and $6x + 8y = 20$ by elimination. Multiply the first equation by $-2$ and add to the second. The result is ___, meaning the system has infinitely many solutions.
3. Which system of equations would produce the result $0 = 0$ when solved by elimination, indicating infinitely many solutions?
- A. $x + 2y = 5$ and $x + 2y = 9$
- B. $2x - y = 3$ and $4x - 2y = 6$
- C. $3x + y = 4$ and $3x + y = 7$
- D. $x - y = 1$ and $2x + y = 5$
4. Solve the system $5x + 2y = 8$ and $10x + 4y = 19$ by elimination. After multiplying the first equation by $-2$ and adding, the result is ___.
5. When both variables are eliminated during elimination by multiplication and the result is a true statement, what geometric relationship do the two lines have?
- A. They are perpendicular and intersect once
- B. They are parallel and never intersect
- C. They are the same line and overlap completely
- D. They intersect at the origin only
6. To eliminate $y$ from the system $2x + 3y = 7$ and $4x + 5y = 11$, what is the LCM of the $y$-coefficients 3 and 5?
- A. 8
- B. 15
- C. 10
- D. 12
7. To eliminate $y$ from $2x + 3y = 7$ and $4x + 5y = 11$, multiply the first equation by 5 and the second by $-3$. After adding the resulting equations, the value of $x$ is ___.
8. Solve the system $4x + 3y = 18$ and $2x + 5y = 16$ by elimination. After finding $x = 3$, substitute back into the first equation to find $y = \_\_\_$.
9. To eliminate $x$ from $3x + 2y = 8$ and $5x + 4y = 14$, which pair of multipliers correctly creates opposite $x$-coefficients?
- A. Multiply first by 5 and second by $-3$
- B. Multiply first by 3 and second by $-5$
- C. Multiply first by 2 and second by $-4$
- D. Multiply first by 4 and second by $-2$
10. Solve the system $3x + 4y = 2$ and $5x + 6y = 2$ using elimination. The solution is $(x, y) = \_\_\_$.