Using the solve command effectively

Let's use solve to find the roots to a simple quadratic equation. We want to use x in our equation, but we have a problem: x has been assigned the value 3:

> x;

To clear that assignment, we could type x := 'x'; which would reset x to just " x ". It's often useful to clear ALL the previous assignments of the current session. That's what the restart command does:

> restart;

Now x is just " x ":

> x;

OK, we are ready to solve our quadratic equation:

> sol := solve( x^2 - 7*x + 6 = 0, x );

As we've seen, Maple returns the solutions of the quadratic, arranged in a sequence. Note also that I named the output sol . It almost always pays to name the output of a command like solve , because then you can refer back to the output by name. The variable sol is a sequence of solutions, and we can pick out either solution as

> sol[1]; sol[2];

You could check that these numbers really solve the quadratic by substituting them back into the equation:

> subs( x = sol[1], x^2 - 7*x + 6 );
subs( x = sol[2], x^2 - 7*x + 6 );

Let's use solve to find the roots of a pair of linear equations, first defining the equations and then solving them:

> eq1 := 2*x - 4*y = 6;
eq2 := x + y = 8;
sols := solve( {eq1, eq2}, {x, y} );

The output of the solve command here is a set (it's enclosed in curly braces {}). The set contains two elements, each of which is an equation

> sols[1]; sols[2];

It is possible to use the entire solution in a substitution command.

> subs( sols, x+y );

It's important to note that the solve command has not actually set x or y equal to the stated values---otherwise we'd have assignment operators, := , instead of equal signs.

Here's another example in which the output from solve is a bit more complicated. Since I assigned values to x and y above, I have to clear their values before using them in equations again:

> restart;
sols:=solve( {x^2 + y^2 = 4, x+y=2}, {x, y} );

In this case there are two solutions. Maple returns them as a sequence, which I named sols ; each element of the sequence is a set enclosed in curly braces {}, and each set consists of two equations. For example, the first solution is

> sols[1];