8
algebra

Solve: {6x4y=143x+2y=17\begin{cases} 6x - 4y = 14 \\ 3x + 2y = 17 \end{cases}

A

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

B

(4,2.5)(4, 2.5)

C

(3,4)(3, 4)

D

(5,43)(5, \frac{4}{3})

Correct Answer: C

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

Step 1: Multiply second by 2: 6x+4y=346x + 4y = 34

Step 2: Add to first: (6x4y)+(6x+4y)=14+34(6x - 4y) + (6x + 4y) = 14 + 3412x=4812x = 48x=4x = 4

  • First: 6(3)4(4)=1816=2 eq146(3) - 4(4) = 18 - 16 = 2 \ eq 14
  • Second: 3(3)+2(4)=9+8=173(3) + 2(4) = 9 + 8 = 17

💡 Strategic Tip: Multiplying by 2 creates +4y+4y to cancel 4y-4y.

**Other choices fail.