\n" );
document.write( "
\n" );
document.write( "Discussion
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "To solve a system of linear equations by substitution, you first solve one
\n" );
document.write( "of the equations for one of the variables to get an expression for that
\n" );
document.write( "variable in terms of the other. Then you substitute this expression into the
\n" );
document.write( "second equation giving you a single equation in a single variable that can be
\n" );
document.write( "solved by ordinary methods
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "Solution
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Solve the first equation for x:
\n" );
document.write( "
\n" );
document.write( "Add -2y to both sides
\n" );
document.write( "
\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Take this expression for x and substitute it into the second equation:
\n" );
document.write( "
\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Now solve:
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Now that you know the value of y, you can substitute it into either of the
\n" );
document.write( "original equations and solve for x
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "So the solution set for the system is the ordered pair (7,3)\r
\n" );
document.write( "\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "Check Answer
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Note that the two lines intersect at the point (7,3)
\n" );
document.write( "