5

Set 8: Linear Functions (Intermediate)

Explanation

Answer: A

Find the intersection point of the lines y=2xy = 2x and y=x+4y = x + 4.

A.

(4,8)(4, 8)

✓ Correct
B.

(2,4)(2, 4)

C.

(4,4)(4, 4)

D.

(4,8)(-4, -8)

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Set equations equal. 1. Equate: 2x=x+42x = x + 4. 2. Solve for x: Subtract xx x=4\rightarrow x = 4. 3. Solve for y: Substitute back y=2(4)=8\rightarrow y = 2(4) = 8. 4. Point: (4,8)(4, 8). Strategic Tip: The intersection point is the solution to the system of equations. Choice B is incorrect because check y=2xy=2 x (4=44 =4) but y=x+4y=x+4 (4=2+44 =2+4) fails. Choice C is incorrect because fails first equation. Choice D is incorrect because fails second equation.

Key Steps:

The correct answer is (4,8)(4, 8)

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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