7

Set 2: Systems of Equations (Intermediate)

Explanation

Answer: D

Solve by elimination: {4x+5y=333x2y=8\begin{cases} 4x + 5y = 33 \\ 3x - 2y = 8 \end{cases}

A.

(5,135)(5, \frac{13}{5})

B.

(6,95)(6, \frac{9}{5})

C.

(7,1)(7, 1)

D.

(4,175)(4, \frac{17}{5})

✓ Correct

Detailed Explanation

Choice D is correct. Choice D is the correct answer. Multiply first by 2 and second by 5. Step 1: Multiply: 8x + 10 y = 66$$15x - 10 y = 40 Step 2: Add: $$$23x = 106x = \frac{106}{23}$$ Non-integer. - First: 4(4) + 5(\frac{17}{5}) = 16 + 17 = 33Second:✓ - Second: 3(4) - 2(\frac{17}{5}) = 12 - \frac{34}{5} = \frac{60-34}{5} = \frac{26}{5} \neq 8$ Strategic Tip: LCM of 5 and 2 is 10. Other choices fail.

Key Steps:

The correct answer is (4,175)(4, \frac{17}{5})

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.
C: Choice C is incorrect and may result from a calculation error.

🎯 Keep Practicing!

Master all sections for your best SAT score