the tables represent two linear functions in a system.

what is the solution to this system?

(1, 0)
(1, 6)
(8, 26)
(8, -22)

Question

the tables represent two linear functions in a system.

what is the solution to this system?

(1, 0)
(1, 6)
(8, 26)
(8, -22)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Linear Function Systems", "Solving Systems from Tables" ], "current_concepts": [ "Systems of Linear Equations", "Linear Function Systems", "Solving Systems from Tables" ] } ## Find the equation of the first linear function $$ \begin{aligned} &m_1 = \frac{18 - 26}{-2 - (-4)} = \frac{-8}{2} = -4\ &b_1 = 10 \quad (\text{from } x=0)\ &y = -4x + 10 \end{aligned} $$ ## Find the equation of the second linear function $$ \begin{aligned} &m_2 = \frac{8 - 14}{-2 - (-4)} = \frac{-6}{2} = -3\ &b_2 = 2 \quad (\text{from } x=0)\ &y = -3x + 2 \end{aligned} $$ ## Solve the system of linear equations $$ \begin{aligned} &-4x + 10 = -3x + 2\ &8 = x\ &y = -3(8) + 2 = -22\ &(x, y) = (8, -22) \end{aligned} $$

(A) $(1, 0)$

(B) $(1, 6)$

(C) $(8, 26)$

(D) $(8, -22)$

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

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QUESTION IMAGE

Question

Explanation:

Find the equation of the first linear function

Find the equation of the second linear function

Solve the system of linear equations

Answer: