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

$x + y = 14$
$x - y = -2$

Question

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

$x + y = 14$
$x - y = -2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "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", "Graphing Linear Equations" ] } ## Set up the system of equations Using the *Systems of Linear Equations* knowledge point We are given the following system of two linear equations: $$ \begin{aligned} (1)\quad &x + y = 14 \ (2)\quad &x - y = -2 \end{aligned} $$ ## Solve for x by elimination Using the *Linear Equations Solving* knowledge point $$ \begin{aligned} (x + y) + (x - y) &= 14 + (-2) \ 2x &= 12 \ x &= 6 \end{aligned} $$ ## Solve for y by substitution Using the *Linear Equations Solving* knowledge point $$ \begin{aligned} 6 + y &= 14 \ y &= 8 \end{aligned} $$ ## Verify the solution Using the *Systems of Linear Equations* knowledge point $$ \begin{aligned} 6 - 8 = -2 \end{aligned} $$ $(6, 8)$ { "elements": [ { "type": "functiongraph", "params": [{"js": "14 - x", "latex": "y = 14 - x"}, -2, 12], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "x + y = 14", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "x + 2", "latex": "y = x + 2"}, -2, 12], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "name": "x - y = -2", "withLabel": true } }, { "type": "point", "params": [[6, 8]], "properties": { "name": "(6, 8)", "size": 4, "color": "#F2557F", "strokeColor": "#F2557F", "fillColor": "#F2557F", "withLabel": true } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Linear Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the system of equations

Solve for x by elimination

Solve for y by substitution

Verify the solution

Answer: