1

Set 13: Linear Functions (Advanced)

Explanation

Answer: A

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

A.

(3,2)(3, 2)

✓ Correct
B.

(2,3)(2, 3)

C.

(4,1)(4, 1)

D.

(3,−2)(3, -2)

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Elimination method. 1. Add equations: (x+y)+(x−y)=5+1→2x=6→x=3(x + y) + (x - y) = 5 + 1 \rightarrow 2 x = 6 \rightarrow x = 3. 2. Substitute: 3+y=5→y=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 because 2−3≠12 -3 \neq 1. Choice C is incorrect because 4−1≠14 -1 \neq 1 (Choice D is incorrect because 3+(−2)≠53 +(-2) \neq 5.

Key Steps:

•

The correct answer is (3,2)(3, 2)

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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