which ordered pair is the solution to the system of linear equations $-5x + y = 26$ and $2x - 7y = 16$?

$(-4, 6)$
$(6, -4)$
$(-4, -6)$
$(-6, -4)$

Question

which ordered pair is the solution to the system of linear equations $-5x + y = 26$ and $2x - 7y = 16$?

$(-4, 6)$
$(6, -4)$
$(-4, -6)$
$(-6, -4)$

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": [ "Substitution Method", "Linear Combination Method" ], "new_concepts": [], "current_concepts": [ "System of Equations", "Substitution Method", "Linear Combination Method" ] } ## Express y in terms of x Using the *Substitution Method* knowledge point $$ \begin{aligned} &-5x + y = 26 \ &y = 5x + 26 \end{aligned} $$ ## Substitute into the second equation Using the *Substitution Method* knowledge point $$ \begin{aligned} &2x - 7(5x + 26) = 16 \ &2x - 35x - 182 = 16 \ &-33x - 182 = 16 \end{aligned} $$ ## Solve for x Using the *Substitution Method* knowledge point $$ \begin{aligned} &-33x = 16 + 182 \ &-33x = 198 \ &x = -6 \end{aligned} $$ ## Solve for y Using the *Substitution Method* knowledge point $$ \begin{aligned} &y = 5(-6) + 26 \ &y = -30 + 26 \ &y = -4 \end{aligned} $$ ## Verify the ordered pair Using the *Substitution Method* knowledge point $$ \begin{aligned} &\text{Ordered pair: } (-6, -4) \ &2(-6) - 7(-4) = -12 + 28 = 16 \quad (\text{True}) \end{aligned} $$

(A) $(-4, 6)$

(B) $(6, -4)$

(C) $(-4, -6)$

(D) $(-6, -4)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "System of Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Express y in terms of x

Substitute into the second equation

Solve for x

Solve for y

Verify the ordered pair

Answer: