Question

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Answer 1

To get the point where they are equal to each other we have to use simultaneous equation solving: i.e y </= x - 5 = y >/= -x -4 (this is a horrible way to set it out but it gets the following point accross: When they are equal to each other and then subtracted from the other, they equal zero. so what you do then is switch the "less than" or "greater than" symbols for equal signs and you will get functions that are easier to work. Subtracting on from the other (doesn't matter which way round) we get:

y = y
x - 5 = - x - 4
2x - 1 = 0
x = 1/2

so at x = 1/2 they meet. The y value for this can be found from either equations (as they are equal to each other) giving

y = 1/2 - 5 = -4.5

Now we have to figure out which region the Inequalities both cover (to the left, top, right or bottom) in terms of the point (0.5, -4.5)

Now we know that the condition for this is either x </= 0.5 or x >/= 0.5 as the the region will be to the right or left (or vertically up or down? but I think that will happen if we are saying x < y +5 or something like that perhaps) of that point and that y = 4.5 is a condition they both share.

Remember that y </= x means that y is equal all values on and Below the graph of y = x and that the opposite would count for y >/= x

So if we consider where the coordinate values to the right and to the left hold true we can get an idea of where to look.

taking y </= x - 5 and putting x = 0 (to the left of the point where they meet) and keeping y= -4.5 (as we are looking at the straight line through (0.5, -4.5) and y can be any value below the graph), we get:

-4.5 </= 0 - 5
-4.5 </= -5

But taking x = 1 (to the right of 0.5) we get

-4.5 </= 1 - 5
-4.5 </= -4 which is correct so x >/= 0.5 is looking like a good condition!

Now we try and see if both are correct within these parameters, with again equaling -4.5 and x = 2 (just a random number to the right of 0.5)

- 4.5 >/= - 2 - 4
- 4.5 >/= - 6 Which is correct!

so we have or parameter x >/= 0.5 so we can easily see that (-5, 2) and (5, -2) are not acceptable coordinates.

Answer 2

I basically just plagiarised the entire internet into that one answer! Was much more difficult than I anticipated haha

Answer 3

To figure out whether (5, -2) or (5, 2) is the correct answer (since I'm assuming you won't get a lot of points for just inputting the possible values otherwise this question is really very easy) you just have to test whether the graph of y = x - 5 (as y has to lie below it and it'll cut the x-axis to the right (positive) of the origin thanks to it's positive gradient).

This of course is done by setting y = 0 giving

x - 5 = 0
x = 5 so x cuts the x axis at (5, 0) so clearly (5, 0) is not an acceptable answer as y lies below or is equal to the y values of y = x - 5. This leaves us with the answer of (5, -2). Out of how much does this question btw? or does it not say?

Answer 4

thank you :)