1

Set 11: Linear Equations (Intermediate)

Explanation

Answer: C

If 3x+4y=203x + 4y = 20 and x2y=10x - 2y = 10, what is x+yx + y?

A.

5

B.

8

C.

7

✓ Correct
D.

6

Detailed Explanation

Choice C is correct. Choice C is the correct answer. 1. Solve System: Multiply 2 nd \neq by 2: 2x4y=202x - 4 y = 20 2. Add to 1 st: (3x+4y)+(2x4y)=20+205x=40x=8(3 x + 4 y) + (2 x - 4 y) = 20 + 20 \rightarrow 5 x = 40 \rightarrow x = 8 3. Find y: 82y=102y=2y=18- 2 y = 10 \rightarrow -2 y = 2 \rightarrow y = -1 4. Calculate: x+y=8+(1)=7x + y = 8 + (-1) = 7 Choice A is incorrect because it results from an error in the solution process. Choice C is incorrect because it results from an error in the solution process. Choice D is incorrect because it results from an error in the solution process.

Key Steps:

The correct answer is 7

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