document.write( "Question 19796: System of equations
\n" ); document.write( "3x+2y=1
\n" ); document.write( "2x-3y=2 \n" ); document.write( "

Algebra.Com's Answer #9560 by xcentaur(357) $\"\"$ $\"About$

You can put this solution on YOUR website!
3x+2y=1.....[multiply by 2]
\n" ); document.write( "2x-3y=2.....[multiply by 3]
\n" ); document.write( "

\n" ); document.write( "we multiply the equations to make the x variable equal
\n" ); document.write( "the first one becomes 3x*2=6x,and the second becomes 2x*3=6x
\n" ); document.write( "Then we can subtract and eliminate them
\n" ); document.write( "note that the equations do not change if you multiply them by a number,because you can always divide them and again get back you original equation.
\n" ); document.write( "

\n" ); document.write( "6x+4y=2
\n" ); document.write( "6x-9y=6
\n" ); document.write( "subtract equation [2] from [1],
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\n" ); document.write( "(6x+4y)-(6x-9y) = 2 - 6
\n" ); document.write( "6x+4y-6x+9y=-4
\n" ); document.write( "13y=-4
\n" ); document.write( "y=-4/13
\n" ); document.write( "

\n" ); document.write( "Now look at eqn [2]
\n" ); document.write( "6x-9y=6
\n" ); document.write( "6x=6+9y
\n" ); document.write( "6x=6+9(-4/13)
\n" ); document.write( " $\"6x=6%2B%28-36%2F13%29\"$
\n" ); document.write( " $\"6x=6-%2836%2F13%29\"$
\n" ); document.write( " $\"6x=%28%2813%2A6%29-36%29%2F13\"$
\n" ); document.write( " $\"6x=%2878-36%29%2F13\"$
\n" ); document.write( " $\"6x=42%2F13\"$
\n" ); document.write( " $\"x=%2842%2F13%29%2F6\"$
\n" ); document.write( " $\"x=42%2F%2813%2A6%29\"$
\n" ); document.write( " $\"x=7%2F13\"$
\n" ); document.write( "

\n" ); document.write( "x=7/13,y=-4/13
\n" ); document.write( "

\n" ); document.write( "Hope this helps,
\n" ); document.write( "Prabhat \n" ); document.write( "

\n" );