6
algebra

Solve by elimination: {4x+5y=333x2y=8\begin{cases} 4x + 5y = 33 \\ 3x - 2y = 8 \end{cases}

A

(5,135)(5, \frac{13}{5})

B

(6,95)(6, \frac{9}{5})

C

(7,1)(7, 1)

D

(4,175)(4, \frac{17}{5})

Correct Answer: D

Choice D is the correct answer. Multiply first by 2 and second by 5.

Step 1: Multiply: 8x+10y=668x + 10y = 6615x10y=4015x - 10y = 40

Step 2: Add: 23x=10623x = 106x=10623x = \frac{106}{23}

Non-integer. - First: 4(4)+5(175)=16+17=334(4) + 5(\frac{17}{5}) = 16 + 17 = 33

  • Second: 3(4)2(175)=12345=60345=265 eq83(4) - 2(\frac{17}{5}) = 12 - \frac{34}{5} = \frac{60-34}{5} = \frac{26}{5} \ eq 8

💡 Strategic Tip: LCM of 5 and 2 is 10.

**Other choices fail.