document.write( "Question 1066683: 8x-6y=12
\n" ); document.write( "12x-9y=18
\n" ); document.write( "Solve and show check \n" ); document.write( "

Algebra.Com's Answer #681901 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!


\n" );
document.write( "8x-6y = 12   (1)
\n" );
document.write( "12x-9y = 18  (2)\r
\n" );
document.write( "\n" );
document.write( "Multiply equation (1) by 3/2:    (3/2)(8x-6y) = (3/2)(12)
\n" );
document.write( "                                     12x - 9y = 18\r
\n" );
document.write( "\n" );
document.write( "See how it matches equation (2).  This means the two equations are linearly dependent.   That means you really only have one equation with two unknowns (infinite number of solutions).  The solutions correspond to a line, and that line has equation  12x-9y = 18  or, in slope-intercept form:
\n" );
document.write( " 
\n" );
document.write( "                    -9y = 18 - 12x
\n" );
document.write( "                          
\n" );
document.write( "                         
\n" );
document.write( "                            -2 is the y-axis intercept
\n" );
document.write( "                            12/9 is the slope
\n" );
document.write( "                       Here is a graph of the line:\r
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( "

\n" );