10
algebra

Find the intersection of x+y=5x + y = 5 and xy=1x - y = 1.

A

(3,2)(3, 2)

B

(2,3)(2, 3)

C

(4,1)(4, 1)

D

(3,2)(3, -2)

Correct Answer: A

Choice A is the correct answer. Elimination method.

  1. Add equations: (x+y)+(xy)=5+12x=6x=3(x + y) + (x - y) = 5 + 1 \rightarrow 2x = 6 \rightarrow x = 3.
  2. Substitute: 3+y=5y=23 + y = 5 \rightarrow y = 2.
  3. Point: (3,2)(3, 2).

💡 Strategic Tip: Adding equations is often faster than substitution.

Choice B is incorrect because23eq12-3 eq 1. Choice C is incorrect because41eq14-1 eq 1 (wait, 41=3eq14-1=3 eq 1). Choice D is incorrect because3+(2)eq53+(-2) eq 5.