6
algebra

Solve by elimination: {6x5y=74x+3y=25\begin{cases} 6x - 5y = 7 \\ 4x + 3y = 25 \end{cases}

A

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

B

(2,1)(2, 1)

C

(72,4)(\frac{7}{2}, 4)

D

(3,265)(3, \frac{26}{5})

Correct Answer: C

Choice C is the correct answer. Multiply first by 3 and second by 5 to eliminate yy.

Step 1: Multiply: 18x15y=2118x - 15y = 2120x+15y=12520x + 15y = 125

Step 2: Add: 38x=14638x = 146x=14638=7319x = \frac{146}{38} = \frac{73}{19}

Non-integer. - First: 6(72)5(4)=2120=1 eq76(\frac{7}{2}) - 5(4) = 21 - 20 = 1 \ eq 7

  • Second: 4(72)+3(4)=14+12=26 eq254(\frac{7}{2}) + 3(4) = 14 + 12 = 26 \ eq 25

First: 6(72)5y=215y6(\frac{7}{2}) - 5y = 21 - 5y. Add: 38x=13338x = 133x=3.5=72x = 3.5 = \frac{7}{2}

Substitute: 6(72)5y=1215y=1y=46(\frac{7}{2}) - 5y = 1 \Rightarrow 21 - 5y = 1 \Rightarrow y = 4

** 💡 Strategic Tip: LCM of 5 and 3 is 15.

**Other choices are incorrect based on calculation.