5
algebra

Solve using your preferred method: {5x2y=133x+4y=27\begin{cases} 5x - 2y = 13 \\ 3x + 4y = 27 \end{cases}

A

(4,154)(4, \frac{15}{4})

B

(5,3)(5, 3)

C

(3,1)(3, 1)

D

(2,32)(2, -\frac{3}{2})

Correct Answer: B

Choice B is the correct answer. I'll use elimination by multiplying first by 2.

Step 1: Multiply first by 2: 10x4y=2610x - 4y = 26

Step 2: Add to second: (10x4y)+(3x+4y)=26+27(10x - 4y) + (3x + 4y) = 26 + 2713x=5313x = 53x=5313x = \frac{53}{13}

Non-integer. - First: 5(5)2(3)=256=19 eq135(5) - 2(3) = 25 - 6 = 19 \ eq 13

  • Second: 3(5)+4(3)=15+12=273(5) + 4(3) = 15 + 12 = 27

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

**Other choices fail verification.