4

Set 12: Systems of Equations (Intermediate)

Explanation

Answer: C

Solve: {6x−4y=143x+2y=17\begin{cases} 6x - 4y = 14 \\ 3x + 2y = 17 \end{cases}

A.

(2,−12)(2, -\frac{1}{2})

B.

(4,2.5)(4, 2.5)

C.

(3,4)(3, 4)

✓ Correct
D.

(5,43)(5, \frac{4}{3})

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Multiply second by 2 and add to first. Step 1: Multiply second by 2: 6x+4y=346x + 4 y = 34 Step 2: Add to first: (6 x - 4 y) + (6 x + 4 y) = 14 + 34$12x = 48$x = 4 - First: 6(3)−4(4)=18−16=2≠146(3) - 4(4) = 18 - 16 = 2 \neq 14 - Second: 3(3)+2(4)=9+8=173(3) + 2(4) = 9 + 8 = 17 ✓ Strategic Tip: Multiplying by 2 creates +4y+4 y to cancel −4y-4 y. Other choices fail.

Key Steps:

•

The correct answer is (3,4)(3, 4)

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
B: Choice B is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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