4
algebra

Solve: {x=3y+12x+5y=13\begin{cases} x = 3y + 1 \\ 2x + 5y = 13 \end{cases}

A

(7,2)(7, 2)

B

(4,1)(4, 1)

C

(10,3)(10, 3)

D

(5,43)(5, \frac{4}{3})

Correct Answer: A

Choice A is the correct answer. Since x=3y+1x = 3y + 1 is already isolated, substitute directly.

Step 1: Substitute into second equation: 2(3y+1)+5y=132(3y + 1) + 5y = 136y+2+5y=136y + 2 + 5y = 1311y=1111y = 11y=1y = 1

  • First: 4=3(1)+1=44 = 3(1) + 1 = 4
  • Second: 2(4)+5(1)=8+5=132(4) + 5(1) = 8 + 5 = 13

Choice B is incorrect because2(4)+5(1)=13 eq242(4) + 5(1) = 13 \ eq 24.

Choice C is incorrect because2(10)+5(3)=35 eq242(10) + 5(3) = 35 \ eq 24.

**Choice D is incorrect.