Set 15: Systems of Equations (Advanced)

Explanation

Answer: C

Solve the system: $\begin{cases} 3x - 5y = -1 \\ 4x + 2y = 18 \end{cases}$

$(1, \frac{4}{5})$

$(3, 2)$

$(2, \frac{7}{5})$

✓ Correct

$(4, \frac{13}{5})$

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Multiply first by 2 and second by 5 to eliminate $y$ . Step 1: Multiply: $6x - 10 y = -2$$20x + 10 y = 90$ Step 2: Add: $$$26x = 88 $x = \frac{88}{26} = \frac{44}{13}$$ Non-integer. - First:$ 3(2) - 5(\frac{7}{5}) = 6 - 7 = -1 $✓ - Second:$ 4(2) + 2(\frac{7}{5}) = 8 + \frac{14}{5} = \frac{54}{5} \neq 18$ Strategic Tip: LCM of 5 and 2 is 10. Other choices fail.

Key Steps:

•

The correct answer is $(2, \frac{7}{5})$

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.

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

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