Simultaneous equations

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value. Can you find that x, y pair?

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?

Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.