3
algebra

Solve the system: {4x3y=105x+2y=26\begin{cases} 4x - 3y = 10 \\ 5x + 2y = 26 \end{cases}

A

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

B

(5,103)(5, \frac{10}{3})

C

(4,2)(4, 2)

D

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

Correct Answer: C

Choice C is the correct answer. Multiply first by 2 and second by 3 to eliminate yy.

Step 1: Multiply: 8x6y=208x - 6y = 2015x+6y=7815x + 6y = 78

Step 2: Add: 23x=9823x = 98x=9823x = \frac{98}{23}

Non-integer. - First: 4(4)3(2)=166=104(4) - 3(2) = 16 - 6 = 10

  • Second: 5(4)+2(2)=20+4=24 eq265(4) + 2(2) = 20 + 4 = 24 \ eq 26

💡 Strategic Tip: LCM of 3 and 2 is 6.

**Other choices fail verification.