q. which ordered pair is the solution to the system?

\\begin{cases} -2x + y = -7 \\ -4x - 3y = 11 \end{cases}\

a. $(-2, -1)$
b. $(3, -1)$
c. $(2, -3)$
d. $(1, -5)$

Question

q. which ordered pair is the solution to the system?

\\begin{cases} -2x + y = -7 \\ -4x - 3y = 11 \end{cases}\

a. $(-2, -1)$
b. $(3, -1)$
c. $(2, -3)$
d. $(1, -5)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Systems of Equations", "Substitution Method" ], "new_concepts": [], "current_concepts": [ "Systems of Equations", "Substitution Method", "Elimination Method" ] } ## Express y in terms of x Using the *Substitution Method* and *Systems of Equations* knowledge points $$ \begin{aligned} &-2x + y = -7 \ &y = 2x - 7 \end{aligned} $$ ## Substitute into the second equation Using the *Substitution Method* and *Systems of Equations* knowledge points $$ \begin{aligned} &-4x - 3(2x - 7) = 11 \ &-4x - 6x + 21 = 11 \ &-10x + 21 = 11 \end{aligned} $$ ## Solve for x Using the *Substitution Method* and *Systems of Equations* knowledge points $$ \begin{aligned} &-10x = 11 - 21 \ &-10x = -10 \ &x = 1 \end{aligned} $$ ## Solve for y Using the *Substitution Method* and *Systems of Equations* knowledge points $$ \begin{aligned} &y = 2(1) - 7 \ &y = 2 - 7 \ &y = -5 \end{aligned} $$ ## Verify the solution Using the *Systems of Equations* knowledge point $$ \begin{aligned} &-4(1) - 3(-5) = -4 + 15 = 11 \quad (\text{True}) \end{aligned} $$ The solution is $(1, -5)$.

(A) $(-2, -1)$

(B) $(3, -1)$

(C) $(2, -3)$

(D) $(1, -5)$

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Explanation:

Express y in terms of x

Substitute into the second equation

Solve for x

Solve for y

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Answer: