solve the following systems of equations for the unknown variables. enter your answer in (x, y) format.

$x - 3 = 2y$
$x + y = 18$

Question

solve the following systems of equations for the unknown variables. enter your answer in (x, y) format.

$x - 3 = 2y$
$x + y = 18$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Systems of Linear Equations", "Algebraic Substitution" ], "new_concepts": [], "current_concepts": [ "Systems of Linear Equations", "Algebraic Substitution" ] } ## Express x in terms of y Using the *Systems of Linear Equations* knowledge point $$ \begin{aligned} &x - 3 = 2y \ &x = 2y + 3 \end{aligned} $$ ## Substitute x into the second equation Using the *Algebraic Substitution* knowledge point $$ \begin{aligned} &(2y + 3) + y = 18 \ &3y + 3 = 18 \end{aligned} $$ ## Solve for y Using the *Basic Arithmetic Operations* knowledge point $$ \begin{aligned} &3y = 15 \ &y = 5 \end{aligned} $$ ## Solve for x Using the *Algebraic Substitution* knowledge point $$ \begin{aligned} &x = 2(5) + 3 \ &x = 13 \end{aligned} $$ ## Verify the solution Using the *Basic Arithmetic Operations* knowledge point $$ \begin{aligned} &13 + 5 = 18 \quad (\text{True}) \ &13 - 3 = 2(5) \quad (\text{True}) \end{aligned} $$ Solve the following systems of equations for the unknown variables. Enter your answer in (x, y) format. Answer: $(13, 5)$ { "elements": [ { "type": "functiongraph", "params": [ { "js": "0.5 * x - 1.5", "latex": "y = \frac{x - 3}{2}" }, -2, 18 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "x - 3 = 2y", "withLabel": true } }, { "type": "functiongraph", "params": [ { "js": "18 - x", "latex": "y = 18 - x" }, -2, 18 ], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "name": "x + y = 18", "withLabel": true } }, { "type": "point", "params": [ [13, 5] ], "properties": { "name": "(13, 5)", "size": 4, "color": "#583C87", "withLabel": true } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Express x in terms of y

Substitute x into the second equation

Solve for y

Solve for x

Verify the solution

Answer: