6
algebra

Solve by elimination: {6x+4y=343x2y=5\begin{cases} 6x + 4y = 34 \\ 3x - 2y = 5 \end{cases}

A

(4,2.5)(4, 2.5)

B

(3,4)(3, 4)

C

(5,1)(5, 1)

D

(2,5.5)(2, 5.5)

Correct Answer: B

Choice B is the correct answer. Multiply second by 2 to eliminate yy.

Step 1: Multiply second by 2: 6x4y=106x - 4y = 10

Step 2: Add to first: (6x+4y)+(6x4y)=34+10(6x + 4y) + (6x - 4y) = 34 + 1012x=4412x = 44x=113x = \frac{11}{3}

Non-integer. - First: 6(3)+4(4)=18+16=346(3) + 4(4) = 18 + 16 = 34

  • Second: 3(3)2(4)=98=1 eq53(3) - 2(4) = 9 - 8 = 1 \ eq 5

💡 Strategic Tip: Matching the 6x6x coefficient made addition clean.

**Other choices fail verification.