(Note about browsers: This page requires Java. I have successfully tested this page using Chrome and Firefox. I cannot get it to run on Internet Explorer.)
Two Lines (look lower for three planes)====
Two lines in the plane can meet in a point (one solution), be the same line (infinitely many solutions), or run parallel to each other and never intersect (no solution). The code below allows you to visualize this.
<sagecell> var('x,y')
- Type your equations. Use == as the equal sign in your equation.
eqn1 = 2*x+3*y==4 eqn2 = 1*x-5*y==6
- This code creates a plot of your equations. You may need to change the bounds.
p=implicit_plot(eqn1,(x,-10,10),(y,-10,10),color='red') p+=implicit_plot(eqn2,(x,-10,10),(y,-10,10),color='blue') show(p)
- This code solves the equations. The output is shown below the plot.
solve([eqn1,eqn2],x,y) </sagecell>
Three Planes====
Three planes in space can meet in a point (one solution), a line (infinitely many solutions), be the same plane (infinitely many solutions), or not meet at all (no solution). The code below allows you to visualize this.
<sagecell> var('x,y,z')
- Type your equations. Use == as the equal sign in your equation.
eqn1 = 2*x+3*y+4*z==4 eqn2 = 1*x-5*y==6 eqn3 = -x+y+2*z==0
- This code creates a plot of your equations. You may need to change the bounds.
p=implicit_plot3d(eqn1,(x,-10,10),(y,-10,10),(z,-10,10),color='red') p+=implicit_plot3d(eqn2,(x,-10,10),(y,-10,10),(z,-10,10),color='green') p+=implicit_plot3d(eqn3,(x,-10,10),(y,-10,10),(z,-10,10),color='blue') show(p)
- This code solves the equations. The output is shown below the plot.
solve([eqn1,eqn2,eqn3],x,y,z) </sagecell>
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