For the system of equations below, which method is most efficient and why? $$ \begin{cases} 4a - 5b = 12 \\ -4a + 3b = -8 \end{cases} $$

Substitution, because one equation is already solved for a variable.

Elimination, because the coefficients of the variable $a$ are opposites.

Substitution, because the constant terms are 12 and -8.

Elimination, because the coefficients of the variable $b$ are the same.

Which characteristic of a system of linear equations most strongly suggests using the elimination method?

One equation is already solved for one variable.

Both equations are in standard form ($Ax+By=C$) and the coefficients of one variable are opposites.

The constant terms in both equations are identical.

Solving Systems of Equations by Elimination Practice — Grade 11 math

Lesson 3: Solving Systems of Equations by Elimination — Practice Questions

1. Which method is most convenient for solving this system of equations? $$ \begin{cases} x = 3y - 2 \\ 2x + 5y = 7 \end{cases} $$
- A. Substitution
- B. Elimination
- C. Both are equally convenient
- D. Neither method is convenient
2. For the system of equations below, which method is most efficient and why? $$ \begin{cases} 4a - 5b = 12 \\ -4a + 3b = -8 \end{cases} $$
- A. Substitution, because one equation is already solved for a variable.
- B. Elimination, because the coefficients of the variable $a$ are opposites.
- C. Substitution, because the constant terms are 12 and -8.
- D. Elimination, because the coefficients of the variable $b$ are the same.
3. Consider the system of equations: $3x + 4y = 11$ and $2x - y = 0$. The most convenient method to begin solving this system is ___.
4. Which characteristic of a system of linear equations most strongly suggests using the elimination method?
- A. One equation is already solved for one variable.
- B. Both equations are in standard form ($Ax+By=C$) and the coefficients of one variable are opposites.
- C. The constant terms in both equations are identical.
- D. The variables are $x$ and $y$.
5. For the system $2x + 3y = 5$ and $6x - 5y = 1$, the most direct method to use is ___, because both equations are in standard form.
6. 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 $(0, 8)$.
7. Consider the system: $2x - y = 4$ and $-6x + 3y = -10$. After multiplying the first equation by 3 and adding the equations, the result is $0 = \_\_\_$.
8. 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
9. 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.
10. Using elimination on the system $x + 5y = 3$ and $-2x - 10y = -6$, both variables cancel out. The resulting equation is $0 = \_\_\_$.