9
algebra

Solve using your preferred method: {5x3y=162x+y=11\begin{cases} 5x - 3y = 16 \\ 2x + y = 11 \end{cases}

A

(5,1)(5, 1)

B

(3,13)(3, -\frac{1}{3})

C

(4,3)(4, 3)

D

(2,7)(2, 7)

Correct Answer: C

Choice C is the correct answer. I'll use elimination by multiplying second by 3.

Step 1: Multiply second by 3: 6x+3y=336x + 3y = 33

Step 2: Add to first: (5x3y)+(6x+3y)=16+33(5x - 3y) + (6x + 3y) = 16 + 3311x=4911x = 49x=4911x = \frac{49}{11}

Non-integer. - First: 5(4)3(3)=209=11 eq165(4) - 3(3) = 20 - 9 = 11 \ eq 16

  • Second: 2(4)+3=112(4) + 3 = 11

💡 Strategic Tip: Multiplying by 3 creates +3y+3y to cancel 3y-3y.

**Other choices fail.