Re: How to use the result of Solve in Plot?

*To*: mathgroup at smc.vnet.net*Subject*: [mg111649] Re: How to use the result of Solve in Plot?*From*: Helen Read <hpr at together.net>*Date*: Mon, 9 Aug 2010 05:12:23 -0400 (EDT)*References*: <i3m3sv$hi4$1@smc.vnet.net>*Reply-to*: HPR <read at math.uvm.edu>

On 8/8/2010 7:19 AM, Eduardo M. A. M.Mendes wrote: > Hello > > I want to use the result of Solve[{5*x+4*y==12},{y}] in Plot[.,{x,0,2}]. > Plot[Solve[.],{x,0,2}] does not work. The results of Solve are given as a list of replacement rules. For example, try the following. Solve[14 x^2 - 17 x - 6 == 0, x] The output looks like this: {{x -> -(2/7)}, {x -> 3/2}} This is a list of replacement rules, {x->-2/7} and {x->3/2} Here is how we evaluate x according to a replacement rule. x/.{x->-2/7} x/.{x->3/2} So to get the solutions out of Solve, we do this. x /. Solve[14 x^2 - 17 x - 6 == 0, x] You might want to name them when you do it. solns=x /. Solve[14 x^2 - 17 x - 6 == 0, x] Try putting solns in a new cell and evaluate. See? You can also pick out the solutions individually, like this. a=x /. Solve[14 x^2 - 17 x - 6 == 0, x][[1]] b=x /. Solve[14 x^2 - 17 x - 6 == 0, x][[2]] Plot[14x^2-17x-6,{x,a,b}] Now, go back to your example. For starters, you don't need all those curly braces, since you have only one equation and one variable to solve for. (If you have a list of equations to solve simultaneously, and a list of variables to solve for, enclose the list of equations and the list of variables in curly braces.) So you can enter your equation more simply, like this. Solve[5*x + 4*y == 12, y] Now, the result is given in the form of a list of replacement rules. You want to evaluate y according to the replacement rule given by the first solution (which in the example is the only solution). Since the result is a function, rather than naming it the way we did in the previous example, let's define the solution as a function of x. f[x_] = y /. Solve[5*x + 4*y == 12, y][[1]] Plot[f[x], {x, 0, 2}] -- Helen Read University of Vermont