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Set 7: Systems of Equations (Intermediate)

Explanation

Answer: B

Solve by elimination: {5x+3y=282xy=5\begin{cases} 5x + 3y = 28 \\ 2x - y = 5 \end{cases}

A.

(3,133)(3, \frac{13}{3})

B.

(5,1)(5, 1)

✓ Correct
C.

(4,83)(4, \frac{8}{3})

D.

(6,23)(6, -\frac{2}{3})

Detailed Explanation

Choice B is correct. Choice B is the correct answer. Multiply second by 3 to eliminate yy. Step 1: Multiply second by 3: 6x3y=156x - 3 y = 15 Step 2: Add to first: (5 x + 3 y) + (6 x - 3 y) = 28 + 15$11x = 43$x = \frac{43}{11} Non-integer. - First: 5(5)+3(1)=25+3=285(5) + 3(1) = 25 + 3 = 28 ✓ - Second: 2(5)1=101=952(5) - 1 = 10 - 1 = 9 \neq 5 Strategic Tip: Multiplying by 3 creates 3y-3 y to cancel +3y+3 y. Other choices fail verification.

Key Steps:

The correct answer is (5,1)(5, 1)

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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