2
algebra

Solve by elimination: {5x+3y=282xy=5\begin{cases} 5x + 3y = 28 \\ 2x - y = 5 \end{cases}

A

(3,133)(3, \frac{13}{3})

B

(5,1)(5, 1)

C

(4,83)(4, \frac{8}{3})

D

(6,23)(6, -\frac{2}{3})

Correct Answer: B

Choice B is the correct answer. Multiply second by 3 to eliminate yy.

Step 1: Multiply second by 3: 6x3y=156x - 3y = 15

Step 2: Add to first: (5x+3y)+(6x3y)=28+15(5x + 3y) + (6x - 3y) = 28 + 1511x=4311x = 43x=4311x = \frac{43}{11}

Non-integer. - First: 5(5)+3(1)=25+3=285(5) + 3(1) = 25 + 3 = 28

  • Second: 2(5)1=101=9 eq52(5) - 1 = 10 - 1 = 9 \ eq 5

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

**Other choices fail verification.