Solving Systems of Linear Equations by Elimination: 동영상 및 연습문제

Which of the following best summarizes the reason why we must write both equations in standard form (ax + by = c) and align like terms vertically before we can perform the elimination method?

Choose the correct multiplier that is needed to eliminate x in the system: 12x - 5y = 24 and 3x - 2y = 6 when using the factor/multiple strategy. Which equation should be multiplied, and by what scalar (making sure to including the sign), to make the x coefficients cancel-out?

You are given the system: y = 4x - 3 and 6x + 2y = 20. Which method: substitution or elimination, would be considered the most efficient to solve this system of equations and why?

Given the system of equations:

$\{\begin{array}{c}8x+11y=35\\ 14x+33y=85\end{array}$

If you plan to solve the system using the elimination method and want to keep the multipliers as small as possible, which variable should you eliminate first?

Solve the system by elimination:

$\{\begin{array}{c}2x+5y=11\\ -2x+3y=1\end{array}$

You are given the system: 4x + 15y = 29 and 9x + 6y = 17. Which variable would you eliminate first in order to minimize the amount of steps needed to solve this problem, and what multiplier(s) would you use?

Suppose you found (x,y) = (2, −1) as a solution for the system 3x + 4y = 2 and x − y = 3. Does (2, −1) satisfy both original equations?

Solve the system by selecting efficient multipliers: 4x − 9y = −5 and 7x + 9y = 44. Then, provide the solution as an ordered pair.

Without solving, which algebraic method would be the most efficient strategy for the system $\{\begin{array}{c}x=3y-4\\ 7x-2y=10\end{array}$, and why?

Consider the system of equations $\{\begin{array}{c}-x+2y=7\\ 3x-6y=-9\end{array}$. Which algebraic method provides the most efficient path to determining the nature of the solution, and why?

Use elimination to solve the system 5x + 2y = 13 and 8x − 7y = −6 by multiplying each equation by the other's x-coefficient. What is the final solution?

Which step should always be performed first when preparing to use the elimination method on a pair of linear equations?

Why is multiplying one entire equation by −1 a valid step in the elimination method?

Which approach is better for solving 4x + 9y = 1 and 2x − 3y = 11: (A) multiply the second equation by −2 to eliminate x, or (B) multiply the first by 1 and second by −1 to eliminate y? Choose the most efficient and justify concisely.

Solve by elimination: $9x-6y=3$ and $3x+4y=11$. What is the final solution?

Solve by elimination: $3(x+2y)=21$ and $4x-5y=1$. What is the final solution?

A student solved a system and reported the solution as $(x,y)=(-2,4)$. The original system was $\{\begin{array}{c}5x-2y=-18\\ -3x+y=10\end{array}$. Check the student's solution by substitution and decide whether it is correct.

When multiplying an entire equation by a scalar in the elimination process, what must you remember to do to every term?

For the system 6x + 7y = 41 and 2x + 21y = 89, decide which variable should be eliminated using the factor/multiple strategy and identify the scalar needed. What elimination will you perform?

Solve the system: $-2x+7y=1$ and $4x-3y=11$. Provide the final ordered pair.

Solve the system of equations: $2(y-x)=10$ and $-x+3y=1$.

A student attempted to solve the system 5x − 2y = 13 and −10x + 4y = −26 by elimination and concluded there are infinitely many solutions. Examine their reasoning and determine whether their conclusion is valid. Show the algebra.

Which method would you choose to solve $\{\begin{array}{c}4x+5y=23\\ x=\frac{1}{2}y+3\end{array}$, and why?