what is the x-value of the solution to the system of equations?

$5x + 4y = 8$
$2x - 3y = 17$

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Question

what is the x-value of the solution to the system of equations?

$5x + 4y = 8$
$2x - 3y = 17$

-3
-2
4
5

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": [ "Systems of Linear Equations", "Elimination Method" ], "current_concepts": [ "Systems of Linear Equations", "Elimination Method" ] } ## Set up the system of equations $$ \begin{cases} 5x + 4y = 8 \quad \text{--- (1)} \ 2x - 3y = 17 \quad \text{--- (2)} \end{cases} $$ ## Eliminate y to solve for x $$ \begin{aligned} 3 \times (1): \quad & 15x + 12y = 24 \ 4 \times (2): \quad & 8x - 12y = 68 \ \text{Add the equations:} \quad & (15x + 12y) + (8x - 12y) = 24 + 68 \ & 23x = 92 \end{aligned} $$ ## Calculate the value of x $$ \begin{aligned} x = \frac{92}{23} = 4 \end{aligned} $$

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

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QUESTION IMAGE

Question

Explanation:

Set up the system of equations

Eliminate y to solve for x

Calculate the value of x

Answer: