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Vladimir [108]
3 years ago
15

How many solutions?

Mathematics
1 answer:
Nadya [2.5K]3 years ago
3 0

Answer: No solutions

The attached graph of the two expressions shows two parallel lines. In order to have a solution, the lines must intersect. Parallel lines never do.

Step-by-step explanation:

When you distribute 3(x - 1) you get

3x - 3 = 3x + 5

Attempting to solve this you get

3x -3x = 5 + 3

0 = 8  False!

0 ≠ 8

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Which linear inequality is shown on the graph?
AlekseyPX
Answer: choice C) x-y <= 2

======================================

Explanation:

The two points (0,-2) and (2,0) are on the boundary line. The boundary line equation is y = x-2. We find this equation through the use of the slope formula to find that m = 1. The y intercept is -2 so b = -2. Therefore, y = mx+b turns into y = 1x+(-2) which simplifies to y = x-2

The equation y = x-2 can be arranged to get x-y = 2 (subtract y from both sides; add 2 to both sides)

So the answer is either x-y <= 2 OR it is x-y >= 2

The question is: which inequality has the test point (0,0) in it? We pick on the origin since 0 is the easiest number to work with.

Plug (x,y) = (0,0) into the equation for choice C
x-y <= 2
0-0 <= 2
0 <= 2
which is true. So choice C is the answer.

Choice D can be ruled out since...
x-y >= 2
0-0 >= 2
0 >= 2
which is false: 0 is not larger or equal to 2
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