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

$2x + y = 18$
$y + z = 3$
$x - z = 9$

Question

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

$2x + y = 18$
$y + z = 3$
$x - z = 9$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Systems of Linear Equations", "Algebraic Substitution" ], "new_concepts": [ "Three Variable Systems" ], "current_concepts": [ "Systems of Linear Equations", "Algebraic Substitution", "Three Variable Systems" ] } ## Express variables in terms of z Using the *Algebraic Substitution* and *Systems of Linear Equations* knowledge points $$ \begin{aligned} &y = 3 - z \ &x = 9 + z \end{aligned} $$ ## Substitute into the first equation Using the *Algebraic Substitution* knowledge point $$ \begin{aligned} &2(9 + z) + (3 - z) = 18 \ &18 + 2z + 3 - z = 18 \ &21 + z = 18 \ &z = -3 \end{aligned} $$ ## Solve for x and y Using the *Algebraic Substitution* knowledge point $$ \begin{aligned} &x = 9 + (-3) = 6 \ &y = 3 - (-3) = 6 \end{aligned} $$ ## Verify the solution Using the *Systems of Linear Equations* knowledge point $$ \begin{aligned} &2(6) + 6 = 12 + 6 = 18 \quad \text{(True)} \ &6 + (-3) = 3 \quad \text{(True)} \ &6 - (-3) = 9 \quad \text{(True)} \end{aligned} $$ $(6, 6, -3)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Linear Equations" ] }

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Question

Explanation:

Express variables in terms of z

Substitute into the first equation

Solve for x and y

Verify the solution

Answer: