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

$x + y = 5$
$x + z = 20$
$y + z = 11$

Question

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

$x + y = 5$
$x + z = 20$
$y + z = 11$

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": [ "Three Variable Systems", "Linear Equations Solving" ], "new_concepts": [], "current_concepts": [ "Three Variable Systems", "Linear Equations Solving" ] } ## Sum the system of equations Using the *Three Variable Systems* and *Linear Equations Solving* knowledge points $$ \begin{aligned} (x + y) + (x + z) + (y + z) &= 5 + 20 + 11 \ 2x + 2y + 2z &= 36 \ x + y + z &= 18 \end{aligned} $$ ## Solve for each variable Using the *Three Variable Systems* and *Linear Equations Solving* knowledge points $$ \begin{aligned} z &= (x + y + z) - (x + y) = 18 - 5 = 13 \ y &= (x + y + z) - (x + z) = 18 - 20 = -2 \ x &= (x + y + z) - (y + z) = 18 - 11 = 7 \end{aligned} $$ ## Verify the solution Using the *Linear Equations Solving* knowledge point $$ \begin{aligned} x + y &= 7 + (-2) = 5 \ x + z &= 7 + 13 = 20 \ y + z &= -2 + 13 = 11 \end{aligned} $$ Solve the following systems of equations for the unknown variables. Enter your answer in (x, y, z) format. $x + y = 5$ $x + z = 20$ $y + z = 11$ $(7, -2, 13)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Three Variable Systems" ] }

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Explanation:

Sum the system of equations

Solve for each variable

Verify the solution

Answer: