home work

$x + y = 3$

$x - y = 9$

what is $x \cdot y$?

Question

home work

$x + y = 3$

$x - y = 9$

what is $x \cdot y$?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "System of Equations", "Elimination Method" ], "new_concepts": [], "current_concepts": [ "System of Equations", "Elimination Method", "Algebraic Substitution" ] } ## Set up the system of equations $$ \begin{cases} x + y = 3 \quad \text{(Equation 1)} \ x - y = 9 \quad \text{(Equation 2)} \end{cases} $$ ## Solve for x by adding the equations $$ \begin{aligned} (x + y) + (x - y) &= 3 + 9 \ 2x &= 12 \ x &= 6 \end{aligned} $$ ## Solve for y by substituting x into Equation 1 $$ \begin{aligned} 6 + y &= 3 \ y &= 3 - 6 \ y &= -3 \end{aligned} $$ $x = 6$, $y = -3$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "System of Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the system of equations

Solve for x by adding the equations

Solve for y by substituting x into Equation 1

Answer: