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Learning Guide Learning Guide

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44 • Chapter 3: Finding Solutions{x = −y, y = y}Here you get only one solution set containing two equations. Thisresult means that y can take any value, while x is the negative of y. Thissolution is parameterized with respect to y.If you give an expression rather than an equation, Maple automaticallyassumes that the expression is equal to zero.> solve({x^3-13*x+12}, {x});{x = 1}, {x = 3}, {x = −4}The solve command can also handle systems of equations.> solve({x+2*y=3, y+1/x=1}, {x,y});{x = −1, y = 2}, {x = 2, y = 1 2 }Although you do not always need the braces (denoting a set) aroundeither the equation or variable, using them forces Maple to return the solutionas a set, which is usually the most convenient form. For example, itis a common practice to check your solutions by substituting them into theoriginal equations. The following example demonstrates this procedure.As a set of equations, the solution is in an ideal form for the subscommand. You might first give the set of equations a name, like eqns, forinstance.> eqns := {x+2*y=3, y+1/x=1};eqns := {x + 2 y = 3, y + 1 x = 1}Then solve.> soln := solve( eqns, {x,y} );soln := {x = −1, y = 2}, {x = 2, y = 1 2 }This produces two solutions:> soln[1];

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