solve the system of equations below.
\\begin{aligned}
3x + 4y &= 10 \\
6x - 2y &= 40
\end{aligned}\

(6, -2)
(-2, -6)
(2, 6)
(2, -6)

Question

solve the system of equations below.
\\begin{aligned}
3x + 4y &= 10 \\
6x - 2y &= 40
\end{aligned}\

(6, -2)
(-2, -6)
(2, 6)
(2, -6)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Systems of Equations Elimination" ], "new_concepts": [], "current_concepts": [ "Systems of Equations Elimination", "Linear Functions" ] } ## Set up the system of equations $$ \begin{cases} 3x + 4y = 10 \quad \text{--- (Equation 1)} \ 6x - 2y = 40 \quad \text{--- (Equation 2)} \end{cases} $$ ## Eliminate the variable y Multiply Equation 2 by 2 and add it to Equation 1: $$ \begin{aligned} 2(6x - 2y) &= 2(40) \ 12x - 4y &= 80 \ \ (3x + 4y) + (12x - 4y) &= 10 + 80 \ 15x &= 90 \ x &= 6 \end{aligned} $$ ## Solve for y Substitute $x = 6$ into Equation 1: $$ \begin{aligned} 3(6) + 4y &= 10 \ 18 + 4y &= 10 \ 4y &= -8 \ y &= -2 \end{aligned} $$

(A) (6,-2)

(B) (-2,-6)

(C) (2,6)

(D) (2,-6)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Equations Elimination" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the system of equations

Eliminate the variable y

Solve for y

Answer: