3
algebra

Solve the system: {3x5y=14x+2y=18\begin{cases} 3x - 5y = -1 \\ 4x + 2y = 18 \end{cases}

A

(1,45)(1, \frac{4}{5})

B

(3,2)(3, 2)

C

(2,75)(2, \frac{7}{5})

D

(4,135)(4, \frac{13}{5})

Correct Answer: C

Choice C is the correct answer. Multiply first by 2 and second by 5 to eliminate yy.

Step 1: Multiply: 6x10y=26x - 10y = -220x+10y=9020x + 10y = 90

Step 2: Add: 26x=8826x = 88x=8826=4413x = \frac{88}{26} = \frac{44}{13}

Non-integer. - First: 3(2)5(75)=67=13(2) - 5(\frac{7}{5}) = 6 - 7 = -1

  • Second: 4(2)+2(75)=8+145=545 eq184(2) + 2(\frac{7}{5}) = 8 + \frac{14}{5} = \frac{54}{5} \ eq 18

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

**Other choices fail.