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3x - y = 2
\n" ); document.write( "y = x - 1
\n" ); document.write( "The first part of the Substitution method is to solve one of the equations for one of the variables. (\"Solve for a variable\" means get that variable all by itself on one side of the equation.) Since the y in the second equation is already \"solved for\" we can proceed to the next step.
\n" ); document.write( "Next we substitute for the \"solved for\" variable in the other equation. So we will substitute for y in the other (i.e. first) equation:
\n" ); document.write( "3x - (x-1) = 2
\n" ); document.write( "Notice the use of parentheses. This is an extremely good habit whenever you make substitutions. In this case, with the minus in front of and the parentheses around x-1 we know that we should subtract both the x and the -1:
\n" ); document.write( "2x + 1 = 2
\n" ); document.write( "Now we solve for x. Subtracting 1 from each side we get:
\n" ); document.write( "2x = 1
\n" ); document.write( "Dividing by 2 we get:
\n" ); document.write( "x = 1/2
\n" ); document.write( "It is easy to think we're finished. But we only have half the answer. We also need the value for y. For this we substitute the value we got for x into wither one of the original equations. I'll pick the 2nd equation:
\n" ); document.write( "y = (1/2) - 1
\n" ); document.write( "(Parentheses!)
\n" ); document.write( "which simplifies to:
\n" ); document.write( "y = -1/2
\n" ); document.write( "So the solution to the system is the single point (1/2, -1/2) \n" ); document.write( "