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You can put this solution on YOUR website!
\n" ); document.write( "There are innumerable ways to solve a system like this algebraically. Different methods will be appropriate for different systems of equations.
\n" ); document.write( "You always want to look for ways to make the problem as easy as possible. In your example, a quick look shows that adding the first two equations together eliminates both y and z, allowing you to find the value of x and thus immediately reduce the system of three equations and three unknowns to a system of two equations and two unknowns.
\n" ); document.write( "4x+y+2z = 24; 2x-y-2z = -6 --> 6x = 18 --> x = 3
\n" ); document.write( "Substitute x=3 into either of the first two equations and the third. (Since you found x=3 using the first two equations, substituting x=3 in those same two equations won't get you anywhere.)
\n" ); document.write( "6-y-2z = -6 --> y+2z = 12;
\n" ); document.write( "-3+2y-z = -4 --> 2y-z = -1
\n" ); document.write( "The solution from the other tutor then uses substitution to finish the problem -- solving one equation for one of the variables and substituting the resulting expression for that variable in the other equation.
\n" ); document.write( "When the two equations are both in the form Ax+By=C, I think a solution using elimination is much easier. Multiply the second equation by 2 and add the two equations to eliminate y:
\n" ); document.write( "y+2z = 12; 4y-2z = -2 --> 5y = 10 --> y = 2
\n" ); document.write( "Then substitute y=2 in either of those last two equations to find z:
\n" ); document.write( "2+2z = 12 --> 2z = 10 --> z = 5
\n" ); document.write( "Answer: x=3; y=2; z=5 \n" ); document.write( "