(A) P=(-3;2)

(B) P=(1;-3)

(C) P=(3;3)

(D) P=(4;4)

(E) P=(3;5)

Explain why, please.

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(A) P=(-3;2)

(B) P=(1;-3)

(C) P=(3;3)

(D) P=(4;4)

(E) P=(3;5)

Explain why, please.

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\(\displaystyle 0<y\)

\(\displaystyle y<2x\)

\(\displaystyle y<7-x\)

Can you find the single given point that does?

the answer is (3;3) Your formula is correct, can you explain how this formula works, please. Depend on which conditions? Does the order of lines matter? Is there a general rule?

\(\displaystyle 0<y\)

\(\displaystyle y<2x\)

\(\displaystyle y<7-x\)

Can you find the single given point that does?

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- Nov 24, 2012

- Messages
- 1,819

Consider a plot of the 3 given lines, with the triangular region bounded by these lines shaded in green:the answer is (3;3) Your formula is correct, can you explain how this formula works, please. Depend on which conditions? Does the order of lines matter? Is there a general rule?

Now, we see that the bottom of the triangle lies along the line \(y=0\) and so the \(y\)-coordinates of all points within the triangle must satisfy:

\(\displaystyle 0<y\)

Next, observe that the left side of the triangle lies along the line \(y=2x\), so all points must be to the right of that line. If we pick such a point like \((1,1)\), and substitute that into the line, we find:

\(\displaystyle 1<2(1)\)

And so all points within the triangle also must satisfy:

\(\displaystyle y<2x\)

Finally, we see the right side of the triangle lies along the line \(y=7-x\) and if we again use the point \((1,1)\), we find:

\(\displaystyle 1<7-1\)

And so all points within the triangle also must satisfy:

\(\displaystyle y<7-x\)

And thus we may conclude that any point \((x,y)\) that simultaneously satisfies all 3 conditions must lie within the triangular region bounded by the 3 given lines.