consider the system of linear equations.

\
\begin{aligned}
7x + 16y &= -2 \\
9x - 4y &= 22
\end{aligned}
\

to use the linear combination method and addition to eliminate the $y$-terms, by which number should the second equation be multiplied?

-4

$-\frac{1}{4}$

$\frac{1}{4}$

4

Question

consider the system of linear equations.

\
\begin{aligned}
7x + 16y &= -2 \\
9x - 4y &= 22
\end{aligned}
\

to use the linear combination method and addition to eliminate the $y$-terms, by which number should the second equation be multiplied?

-4

$-\frac{1}{4}$

$\frac{1}{4}$

4

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Linear Combination Method" ], "new_concepts": [], "current_concepts": [ "System of Equations", "Linear Combination Method" ] } ## Identify the given system of equations Using the *Linear Combination Method* knowledge point $$ \begin{aligned} &\text{Equation 1: } 7x + 16y = -2 \ &\text{Equation 2: } 9x - 4y = 22 \end{aligned} $$ ## Determine the multiplier to eliminate the y-terms Using the *Linear Combination Method* knowledge point $$ \begin{aligned} &\text{Coefficient of } y \text{ in Equation 1: } 16 \ &\text{Coefficient of } y \text{ in Equation 2: } -4 \ &16 + m \cdot (-4) = 0 \implies m = 4 \end{aligned} $$

(A) $-4$

(B) $-\frac{1}{4}$

(C) $\frac{1}{4}$

(D) $4$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Combination Method" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given system of equations

Determine the multiplier to eliminate the y-terms

Answer: