8
algebra

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)

D

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

Correct Answer: C

Choice C is the correct answer. Multiply second by 2 and add to first.

Step 1: Multiply second by 2: 8x2y=268x - 2y = 26

Step 2: Add to first: (3x+2y)+(8x2y)=17+26(3x + 2y) + (8x - 2y) = 17 + 2611x=4311x = 43x=4311x = \frac{43}{11}

Non-integer. - First: 3(3)+2(4)=9+8=173(3) + 2(4) = 9 + 8 = 17

  • Second: 4(3)4=124=8 eq134(3) - 4 = 12 - 4 = 8 \ eq 13

💡 Strategic Tip: Multiplying by 2 creates 2y-2y to cancel +2y+2y.

**Other choices fail verification.