5.3 solving systems of equations by substitution quiz

solve the system using substitution:

$y = 3x - 2$

$x + y = 10$

Question

5.3 solving systems of equations by substitution quiz

solve the system using substitution:

$y = 3x - 2$

$x + y = 10$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Substitution Method" ], "new_concepts": [], "current_concepts": [ "Substitution Method", "Linear Equations" ] } ## Substitute the first equation into the second Using the *Substitution Method* knowledge point $$ \begin{aligned} &y = 3x - 2 \ &x + (3x - 2) = 10 \end{aligned} $$ ## Solve the linear equation for x Using the *Linear Equations* knowledge point $$ \begin{aligned} &4x - 2 = 10 \ &4x = 12 \ &x = 3 \end{aligned} $$ ## Substitute x back to find y Using the *Substitution Method* knowledge point $$ \begin{aligned} &y = 3(3) - 2 \ &y = 9 - 2 \ &y = 7 \end{aligned} $$ Solve the system using substitution: $y = 3x - 2$ $x + y = 10$ (3, 7) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Substitution Method" ] }

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QUESTION IMAGE

Question

Explanation:

Substitute the first equation into the second

Solve the linear equation for x

Substitute x back to find y

Answer: