I am trying to find the point of intersection of the following graphs, and, wondering whether it may help me with the logic behind a graphing dilemma that I have with an economic problem, because somehow I am thinking that the point of intersection for the production possibility curve represents something, but I am not sure what. My tutor is not very helpful via email.

Problem 1 What is the point of intersection of the following functions?

f(x) = 2x + 3

g(x) = 0.5x + 7

When working it out manually the point of intersection is where f(x) = g(x), and, so far I have figured out that this happens where x = 6 although I don't know how to work out the value of y. Initially I thought I would solve 2x + 3 = y, but, this is incorrect according to the graphing software I use to check my answer, since the point of intersection is expected to be where x = 1.57 and y = 6.13, so how do I work this out using algebra?

Problem 2.

Two economies are identical: In each, a unit of labour can make either 3 units of y or 1 unit of x (or

any linear combination of them). A unit of capital can make either 3 units of y or 3 units of x (or

any linear combination of them). In each economy there are 100 units of labour, and 50 units of

capital. Both labour and capital are needed in theproduction process. If economy A chooses to

consume efficiently at a point where y=65 while economy B chooses to consume efficiently at a

point where x=65, the economies will not trade. True or false? Explain.

LSE May 2012 Zone B Q.1a