Set 17: Systems of Equations (Intermediate)

Explanation

Answer: C

Solve the system: $\begin{cases} 4x - 3y = 10 \\ 5x + 2y = 26 \end{cases}$

$(3, \frac{2}{3})$

$(5, \frac{10}{3})$

$(4, 2)$

✓ Correct

$(2, -\frac{2}{3})$

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Multiply first by 2 and second by 3 to eliminate $y$ . Step 1: Multiply: $8x - 6 y = 20$$15x + 6 y = 78$ Step 2: Add: $$$23x = 98 $x = \frac{98}{23}$$ Non-integer. - First:$ 4(4) - 3(2) = 16 - 6 = 10 $✓ - Second:$ 5(4) + 2(2) = 20 + 4 = 24 \neq 26$ Strategic Tip: LCM of 3 and 2 is 6. Other choices fail verification.

Key Steps:

•

The correct answer is $(4, 2)$

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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