what is the value of $x$ in this system of equations? express the answer as a decimal rounded to the nearest tenth.

\
\begin{aligned}
-5x - 12y &= -8 \\
5x + 2y &= 48
\end{aligned}
\

Question

what is the value of $x$ in this system of equations? express the answer as a decimal rounded to the nearest tenth.

\
\begin{aligned}
-5x - 12y &= -8 \\
5x + 2y &= 48
\end{aligned}
\

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": [ "System of Equations", "Linear Combination Method" ], "new_concepts": [], "current_concepts": [ "System of Equations", "Linear Combination Method" ] } ## Eliminate the x variable Using the *Linear Combination Method* and *System of Equations* knowledge points $$ \begin{aligned} (-5x - 12y) + (5x + 2y) &= -8 + 48 \ -10y &= 40 \end{aligned} $$ ## Solve for y Using the *System of Equations* knowledge point $$ \begin{aligned} y &= \frac{40}{-10} \ y &= -4 \end{aligned} $$ ## Substitute y to find x Using the *System of Equations* knowledge point $$ \begin{aligned} 5x + 2(-4) &= 48 \ 5x - 8 &= 48 \ 5x &= 56 \ x &= \frac{56}{5} \ x &= 11.2 \end{aligned} $$ What is the value of $x$ in this system of equations? Express the answer as a decimal rounded to the nearest tenth. 11.2 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "System of Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Eliminate the x variable

Solve for y

Substitute y to find x

Answer: