Find the maximum of xy if 2x+3y=1?

2x + 3y = 1 The rule is you can do any valid operation on both sides of an equation and it will still be equal. Subtract 2x.

3y = -2x + 1 Divide by 3.

y = -2x/3 + 1/3 This equation plots as a straight line. It looks like this: www.wolframalpha.com/input/?i=plot+y+%3D+-2x%2F3+%2B+1%2F3

Now consider the plot of xy.

Y = -2(x^2)/3 + x/3 I used capital Y to avoid confusion. Y is not y. The plot is a parabola and looks like this: www.wolframalpha.com/input/?i=plot++Y+%3D+-2(x%5E2)%2F3+%2B+x%2F3

You can go to wikipedia.org and type "parabola" in the search box to get all knowledge about the figure.