solve this system of equations by using substitution.

\\begin{cases} x = 2y \\ 4x + 2y = 30 \end{cases}\

$(?, \quad)$

Question

solve this system of equations by using substitution.

\\begin{cases} x = 2y \\ 4x + 2y = 30 \end{cases}\

$(?, \quad)$

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": [ "Linear Equations" ], "new_concepts": [ "Systems of Equations", "Substitution Method" ], "current_concepts": [ "Linear Equations", "Systems of Equations", "Substitution Method" ] } ## Identify the given system of equations We are given the following system of linear equations: $$ \begin{cases} x = 2y & \text{(Equation 1)} \ 4x + 2y = 30 & \text{(Equation 2)} \end{cases} $$ Our goal is to find the solution as an ordered pair $(x, y)$. ## Substitute Equation 1 into Equation 2 Using the **Linear Equations** knowledge point $$ \begin{aligned} 4(2y) + 2y &= 30 \ 8y + 2y &= 30 \end{aligned} $$ ## Solve for y Using the **Linear Equations** knowledge point $$ \begin{aligned} 10y &= 30 \ y &= 3 \end{aligned} $$ ## Solve for x Using the **Linear Equations** knowledge point $$ \begin{aligned} x &= 2(3) \ x &= 6 \end{aligned} $$ ## Verify the solution We substitute $x = 6$ and $y = 3$ back into Equation 2 to verify: $$ 4(6) + 2(3) = 24 + 6 = 30 $$ The solution is correct. The ordered pair is $(6, 3)$. Solve this system of equations by using substitution. $$ \begin{cases} x = 2y \ 4x + 2y = 30 \end{cases} $$ (6, 3) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given system of equations

Substitute Equation 1 into Equation 2

Solve for y

Solve for x

Verify the solution

Answer: