]> Exercises

Exercises

Solve and plot the following systems of equations that involve non-linear equations

    Use Commands

  1. − ( x + 1 ) 2 − y = 1
    x + 2 y = − 6

    eq1:=-(x+1)^2-y=1
    eq2:=x+2y=-6
    eqns:={eq1, eq2}
    implicitplot([eq1, eq2], x=-5..0, y=-5..5)
    solve({eq1, eq2}, {x,y})

  2. x + 2 y = 6
    ( x + 1 ) 2 − y = − 1

    eq3:=x+2y=6
    eq4:=(x+1)^2-y=-1
    eqs34:= eq3, eq4
    with(plots):
    implicitplot([eqs34], x=-10..10, y=-2..10)
    sols34:=solve({eq34}, {x,y})
    allvalues(sols34)

  3. PLOT ONLY
    y 3 − x 4 = x + 7
    y = x

    eq5:=y^3-x^4=x+7
    eq6:=y=x
    with(plots):
    implicitplot([eq5, eq6], x=-10..10, y=-10..10)

    Use the right click menu

  1. − ( x + 1 ) 2 − y = 1
    x + 2 y = − 6

    Note: This is the same problem solved in the first commands exercise. Use the same document so you don't have to reassign the equations
    {eq1, eq2}
    (right-click set of equations: solve)
    (right-click set of equations: plots->2D implicit plot->x, y)

  2. x + 2 y = 6
    ( x + 1 ) 2 − y = − 1

    Note: This is the same problem solved in the second commands exercise. Use the same document so you don't have to reassign the equations {eq3, eq4}
    (right-click eqns: Plots->2D implicit plot->x,y)
    (right-click eqns: solve)
    (right-click result: Assign to a name)
    (In pop-up window: sols)
    allvalues(sols)

    Use PlotBuilder assistant to plot only

  1. y 3 − x 4 = x + 7
    y = x

    Note: This is the same problem solved in the third commands exercise. Use the same document so you don't have to reassign the equations. (Open PlotBuilder assistant, add the equations to the expressions window as eq5 and eq6)
    (Hit done, the default plot type is 2D Implicit plot, change the ranges to -10 to 10)
    (Click Plot options and change grid size to 100,100)
    (Click plot)