9
algebra

Solve using your preferred method: {2x+5y=24x2y=1\begin{cases} 2x + 5y = 24 \\ x - 2y = 1 \end{cases}

A

(133,109)(\frac{13}{3}, \frac{10}{9})

B

(7,2)(7, 2)

C

(3,185)(3, \frac{18}{5})

D

(5,145)(5, \frac{14}{5})

Correct Answer: C

Choice C is the correct answer. Use substitution. From second: x=1+2yx = 1 + 2y.

Step 1: Substitute into first: 2(1+2y)+5y=242(1 + 2y) + 5y = 242+4y+5y=242 + 4y + 5y = 249y=229y = 22y=229y = \frac{22}{9}

  • Second: 32(185)=3365=15365=215 eq13 - 2(\frac{18}{5}) = 3 - \frac{36}{5} = \frac{15-36}{5} = -\frac{21}{5} \ eq 1
  • First: 2(3)+5(185)=6+18=242(3) + 5(\frac{18}{5}) = 6 + 18 = 24

** 💡 Strategic Tip: Coefficient of 1 on x makes substitution easy.

**Other choices fail.