solve the following system of equations.
\
\begin{aligned}
8x + 5y &= -2 \\
-3x - 7y &= 11
\end{aligned}
\
\x = \square\
\y = \square\

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equations" ], "new_concepts": [ "Systems of Linear Equations", "Elimination Method" ], "current_concepts": [ "Linear Equations", "Systems of Linear Equations", "Elimination Method" ] } ## Set up the system of equations $$ \begin{aligned} (1)\quad 8x + 5y &= -2 \ (2)\quad -3x - 7y &= 11 \end{aligned} $$ ## Eliminate x to solve for y Multiply equation (1) by 3 and equation (2) by 8: $$ \begin{aligned} 24x + 15y &= -6 \ -24x - 56y &= 88 \end{aligned} $$ Add the two equations: $$ \begin{aligned} -41y &= 82 \ y &= -2 \end{aligned} $$ ## Substitute y back to solve for x Substitute $y = -2$ into equation (1): $$ \begin{aligned} 8x + 5(-2) &= -2 \ 8x - 10 &= -2 \ 8x &= 8 \ x &= 1 \end{aligned} $$ Solve the following system of equations. $$ \begin{aligned} 8x + 5y &= -2 \ -3x - 7y &= 11 \end{aligned} $$ $x =$ 1 $y =$ -2 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Linear Equations" ] }

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Question

Explanation:

Set up the system of equations

Eliminate x to solve for y

Substitute y back to solve for x

Answer: