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

$6x + 3y = 18$
$5x + y = 15$

Question

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

$6x + 3y = 18$
$5x + y = 15$

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", "Linear Equations Solving" ], "new_concepts": [], "current_concepts": [ "Systems of Linear Equations", "Linear Equations Solving", "Point of Intersection" ] } ## Express the system of equations Using the *Systems of Linear Equations* knowledge point $$ \begin{cases} 6x + 3y = 18 \quad \text{--- (Equation 1)} \ 5x + y = 15 \quad \text{--- (Equation 2)} \end{cases} $$ ## Express y in terms of x Using the *Linear Equations Solving* knowledge point $$ y = 15 - 5x \quad \text{--- (Equation 3)} $$ ## Substitute and solve for x Using the *Linear Equations Solving* knowledge point $$ \begin{aligned} 6x + 3(15 - 5x) &= 18 \ 6x + 45 - 15x &= 18 \ -9x &= -27 \ x &= 3 \end{aligned} $$ ## Substitute x to find y Using the *Linear Equations Solving* knowledge point $$ \begin{aligned} y &= 15 - 5(3) \ y &= 0 \end{aligned} $$ ## Verify the solution Using the *Systems of Linear Equations* knowledge point $$ \begin{aligned} 6(3) + 3(0) &= 18 \quad (\text{True}) \ 5(3) + 0 &= 15 \quad (\text{True}) \end{aligned} $$ Solve the following systems of equations for the unknown variables. Enter your answer in (x, y) format. $6x + 3y = 18$ $5x + y = 15$ Answer: $(3, 0)$ { "elements": [ { "type": "functiongraph", "params": [ { "js": "6 - 2*x", "latex": "y = 6 - 2x" }, -2, 6 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "6x + 3y = 18", "withLabel": true } }, { "type": "functiongraph", "params": [ { "js": "15 - 5*x", "latex": "y = 15 - 5x" }, -2, 6 ], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "name": "5x + y = 15", "withLabel": true } }, { "type": "point", "params": [ [3, 0] ], "properties": { "name": "(3, 0)", "size": 4, "color": "#5583F2", "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

Explanation:

Express the system of equations

Express y in terms of x

Substitute and solve for x

Substitute x to find y

Verify the solution

Answer: