document.write( "Question 999480: Please help me solve this 4x4 equation
\n" ); document.write( "w+x+y+z=2
\n" ); document.write( "2w-x-y+2z=7
\n" ); document.write( "2w+3x+2y-z=-2
\n" ); document.write( "3w-2x-y-3z=-2 \n" ); document.write( "

Algebra.Com's Answer #617097 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"w%2Bx%2By%2Bz=2\"$ ..................eq.1
\n" ); document.write( " $\"2w-x-y%2B2z=7\"$ ..................eq.2
\n" ); document.write( " $\"2w%2B3x%2B2y-z=-2\"$ ..................eq.3
\n" ); document.write( " $\"3w-2x-y-3z=-2+\"$ ..................eq.4
\n" ); document.write( "-----------------------\r
\n" ); document.write( "\n" ); document.write( " $\"w%2Bx%2By%2Bz=2\"$ ..................eq.1
\n" ); document.write( " $\"2w-x-y%2B2z=7\"$ ..................eq.2
\n" ); document.write( "------------------add\r
\n" ); document.write( "\n" ); document.write( " $\"w%2Bx%2By%2Bz%2B2w-x-y%2B2z=2%2B7\"$
\n" ); document.write( " $\"3w%2B3z=9\"$
\n" ); document.write( " $\"3%28w%2Bz%29=9\"$
\n" ); document.write( " $\"w%2Bz=3\"$
\n" ); document.write( " $\"w=3-z\"$ ...............1a\r
\n" ); document.write( "\n" ); document.write( " $\"2w%2B3x%2B2y-z=+-2\"$ .....................eq.3..multiply by $\"2\"$
\n" ); document.write( " $\"3w-2x-y-3z=+-2\"$ ......................eq.4.multiply by $\"3\"$
\n" ); document.write( "-------------------------------------------
\n" ); document.write( " $\"4w%2B6x%2B4y-2z=+-4\"$
\n" ); document.write( " $\"9w-6x-3y-9z=-6+\"$
\n" ); document.write( "--------------------------------add
\n" ); document.write( " $\"4w%2B6x%2B4y-2z%2B9w-6x-3y-9z=+-4-6\"$
\n" ); document.write( " $\"13w%2By-11z=+-10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=+11z-13w-10\"$ ............substitute $\"+w\"$ from 1a\r
\n" ); document.write( "\n" ); document.write( " $\"y=+11z-13%283-z%29-10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=+11z-39%2B13z-10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=+24z-49\"$ .............1b\r
\n" ); document.write( "\n" ); document.write( "go to
\n" ); document.write( " $\"w%2Bx%2By%2Bz=2\"$ ..................eq.1, subst. $\"w\"$ from 1a and $\"y\"$ from 1b\r
\n" ); document.write( "\n" ); document.write( " $\"%283-z%29%2Bx%2B%2824z-49%29%2Bz=2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3-z%2Bx%2B24z-49%2Bz=2\"$
\n" ); document.write( " $\"x%2B24z-46=2\"$
\n" ); document.write( " $\"x=46%2B2-24z\"$
\n" ); document.write( " $\"x=48-24z\"$ ...............1c\r
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"2w%2B3x%2B2y-z=+-2\"$ .........eq.3, substitute $\"w\"$ from 1a , $\"y\"$ from 1b, and $\"x\"$ from 1c\r
\n" ); document.write( "\n" ); document.write( " $\"2%283-z%29%2B3%2848-24z%29%2B2%2824z-49%29-z=+-2\"$ ............solve for $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"6-2z%2B144-72z%2B48z-98-z=+-2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-75z%2B48z%2B150-98=+-2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-27z%2B52=+-2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2%2B52=+27z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"54=+27z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=54%2F27\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28z=2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go to 1a substitute $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"w=3-z\"$
\n" ); document.write( " $\"w=3-2\"$
\n" ); document.write( " $\"highlight%28w=1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go to 1b substitute $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=+24z-49\"$ .............1b
\n" ); document.write( " $\"y=+24%2A2-49\"$
\n" ); document.write( " $\"y=+48-49\"$
\n" ); document.write( " $\"highlight%28y=+-1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go to 1c substitute $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=48-24z\"$ ...............1c
\n" ); document.write( " $\"x=48-24%2A2\"$
\n" ); document.write( " $\"x=48-48\"$
\n" ); document.write( " $\"highlight%28x=0%29\"$ \r
\n" ); document.write( "\n" ); document.write( "so, your solutions are:
\n" ); document.write( " $\"highlight%28x=0%29\"$
\n" ); document.write( " $\"highlight%28y=+-1%29\"$
\n" ); document.write( " $\"highlight%28w=1%29\"$
\n" ); document.write( " $\"highlight%28z=2%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );