related questions: lesson 4: systems of equations

select the answers for x and y after solving the system of equations using the elimination method.

q. $\begin{cases} 7x + 22y = -28 \\ 3x - 11y = -12 \end{cases}$

a. $(-4, 0)$
b. $(-4, 1)$
c. $(4, 0)$
d. $(4, -1)$

Question

related questions: lesson 4: systems of equations

select the answers for x and y after solving the system of equations using the elimination method.

q. $\begin{cases} 7x + 22y = -28 \\ 3x - 11y = -12 \end{cases}$

a. $(-4, 0)$
b. $(-4, 1)$
c. $(4, 0)$
d. $(4, -1)$

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": [ "Systems of Equations" ], "new_concepts": [ "Elimination Method" ], "current_concepts": [ "Systems of Equations", "Elimination Method" ] } ## Write down the system of equations Using the *Systems of Equations* knowledge point $$ \begin{aligned} (1) \quad 7x + 22y &= -28 \ (2) \quad 3x - 11y &= -12 \end{aligned} $$ ## Eliminate the y variable Using the *Systems of Equations* knowledge point $$ \begin{aligned} 2 \cdot (3x - 11y) &= 2 \cdot (-12) \ 6x - 22y &= -24 \quad (3) \end{aligned} $$ $$ \begin{aligned} (7x + 22y) + (6x - 22y) &= -28 + (-24) \ 13x &= -52 \end{aligned} $$ ## Solve for x Using the *Systems of Equations* knowledge point $$ \begin{aligned} x &= \frac{-52}{13} \ x &= -4 \end{aligned} $$ ## Solve for y Using the *Systems of Equations* knowledge point $$ \begin{aligned} 3(-4) - 11y &= -12 \ -12 - 11y &= -12 \ -11y &= 0 \ y &= 0 \end{aligned} $$ ## Verify the solution Using the *Systems of Equations* knowledge point $$ \begin{aligned} 7(-4) + 22(0) &= -28 \ -28 + 0 &= -28 \quad (\text{True}) \end{aligned} $$

A. $(-4, 0)$

B. $(-4, 1)$

C. $(4, 0)$

D. $(4, -1)$

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

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QUESTION IMAGE

Question

Explanation:

Write down the system of equations

Eliminate the y variable

Solve for x

Solve for y

Verify the solution

Answer: