7

Set 5: Systems of Equations

Explanation

Answer: C

Solve: {3x+2y=174xy=13\begin{cases} 3x + 2y = 17 \\ 4x - y = 13 \end{cases}

A.

(4,52)(4, \frac{5}{2})

B.

(5,1)(5, 1)

C.

(3,4)(3, 4)

✓ Correct
D.

(6,12)(6, -\frac{1}{2})

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: 8x2y=268x - 2 y = 26 Step 2: Add to first: (3 x + 2 y) + (8 x - 2 y) = 17 + 26$11x = 43$x = \frac{43}{11} Non-integer. - First: 3(3)+2(4)=9+8=173(3) + 2(4) = 9 + 8 = 17 ✓ - Second: 4(3)4=124=8134(3) - 4 = 12 - 4 = 8 \neq 13 Strategic Tip: Multiplying by 2 creates 2y-2 y to cancel +2y+2 y. 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.
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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