6

Set 3: Systems of Equations

Explanation

Answer: B

Solve by elimination: {6x+4y=343x2y=5\begin{cases} 6x + 4y = 34 \\ 3x - 2y = 5 \end{cases}

A.

(4,2.5)(4, 2.5)

B.

(3,4)(3, 4)

✓ Correct
C.

(5,1)(5, 1)

D.

(2,5.5)(2, 5.5)

Detailed Explanation

Choice B is correct. Choice B is the correct answer. Multiply second by 2 to eliminate yy. Step 1: Multiply second by 2: 6x4y=106x - 4 y = 10 Step 2: Add to first: (6 x + 4 y) + (6 x - 4 y) = 34 + 10$12x = 44$x = \frac{11}{3} Non-integer. - First: 6(3)+4(4)=18+16=346(3) + 4(4) = 18 + 16 = 34 ✓ - Second: 3(3)2(4)=98=153(3) - 2(4) = 9 - 8 = 1 \neq 5 Strategic Tip: Matching the 6x6x coefficient made addition clean. Other choices fail verification.

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.
C: Choice C 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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