Exercises

Enter the commands to solve each linear system of equations.

Use Commands

1. Enter these equations $2x+3y=2$ and $3x-4y=9$
   Solve the system and give the name sol1 to the solution
   Plot the two equations on the same figure.

               eq1:=2*x+3*y=2
               eq2:=3*x-4*y=9
               sol1:=solve({eq1, eq2}, {x, y})
               with(plots):
               implicitplot([eq1, eq2], x=-3..3, y=-2..2)
             
           

   Notice that the implicitplot command is required to plot equations. The statement with(plots) is required prior to using the implicitplot command. Alternatively, we could have solved each equation for y and used the plot command to plot each solution expression for y.

2. Enter the equations $2x-y=5$ and $x+2y=5$
   Solve the system and give a name to the solution
   Plot the two equations on the same graph to check solution

               eq8 := 2*x-y=5
               eq9 := x+2*y=5
               eqs89 := eq8, eq9
               sol89 := solve({eqs89}, {x, y})
               with(plots):
               implicitplot([eqs89], x=-10..10, y=-10..10, color=[red,blue])
             
           

3. Plot and find the solution to the following system of equations
   $\begin{array}{l}3x-2y+z=4\\ x+3y+2z=5\\ 2x-2y+3z=5\end{array}$

               eq5 := 3x-2y+z=4
               eq6 := x+3y+2z=5
               eq7 := 2x-2y+3z=5
               eqns := eq5, eq6, eq7
               ranges := x=-5..5, y=-5..5, z=-5..5
               with(plots):
               implicitplot3d([eqns], ranges, color=[red,green,blue],transparency=0.25)
               sol567 := solve({eqns}, {x, y, z})