document.write( "Question 1196448: I've been working on this for hours, but keep taking the wrong path. I need to solve the 4x4 equations:
\n" ); document.write( "2w + x - y + 2z = 10
\n" ); document.write( "-w - 3x + y - 5z = -11
\n" ); document.write( "3w + 5x - 3y + z = 35
\n" ); document.write( "-4w - 2x - 3y - z = 2 \n" ); document.write( "

Algebra.Com's Answer #829278 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"2w+%2B+x+-+y+%2B+2z+=+10\"$ ..............eq.1
\n" ); document.write( " $\"-w+-+3x+%2B+y+-+5z+=+-11\"$ ..............eq.2
\n" ); document.write( " $\"3w+%2B+5x+-+3y+%2B+z+=+35\"$ ..............eq.3
\n" ); document.write( " $\"-4w+-+2x+-+3y+-+z+=+2\"$ ..............eq.4\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "start with\r
\n" ); document.write( "\n" ); document.write( " $\"2w+%2B+x+-+y+%2B+2z+=+10+\"$ ..............eq.1
\n" ); document.write( " $\"-w+-+3x+%2B+y+-+5z+=+-11\"$ ..............eq.2
\n" ); document.write( "_____________________________________add both to eliminate $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2w+%2B+x+-+y+%2B+2z+-w+-+3x+%2B+y+-+5z+=+10+-11\"$
\n" ); document.write( " $\"-3+z+-+2+x+%2B+w=+-1\"$ ............solve for $\"w\"$
\n" ); document.write( " $\"w=+-1%2B3+z+%2B2x+\"$ ........................eq.1a\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now go with\r
\n" ); document.write( "\n" ); document.write( " $\"3w+%2B+5x+-+3y+%2B+z+=+35\"$ ..............eq.3
\n" ); document.write( " $\"-4w+-+2x+-+3y+-+z+=+2\"$ ..............eq.4
\n" ); document.write( "___________________________________subtract eq.4 from eq.3\r
\n" ); document.write( "\n" ); document.write( " $\"3w+%2B+5x+-+3y+%2B+z-%28-4w+-+2x+-+3y+-+z%29+=+35-2\"$
\n" ); document.write( " $\"7w%2B+7x%2B2z++=33\"$ ..........solve for $\"w\"$
\n" ); document.write( " $\"7w++=33-7x-2z\"$
\n" ); document.write( " $\"w++=33%2F7-x-2z%2F7\"$ ..............eq.2a\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "from eq.1a and eq.2a we have\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"-1%2B3+z+%2B2x=33%2F7-x-2z%2F7\"$ ............solve for $\"+z\"$
\n" ); document.write( " $\"2z%2F7%2B3+z+=33%2F7-x%2B1-2x\"$
\n" ); document.write( " $\"%2823%2F7%29+z=40%2F7+-+3+x\"$
\n" ); document.write( " $\"z=%2840%2F7+-+3+x%29%2F%2823%2F7%29\"$
\n" ); document.write( " $\"z=40%2F23+-+%2821%2F23%29x\"$ ..............eq.3a \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "go to \r
\n" ); document.write( "\n" ); document.write( " $\"w=+-1%2B3+z+%2B2x\"$ ........................eq.1a, substitute $\"z+\"$
\n" ); document.write( " $\"w=+-1%2B3+%2840%2F23+-+%2821%2F23%29x%29+%2B2x+\"$
\n" ); document.write( " $\"w=+97%2F23+-+%2817%2F23+%29x\"$ ..........eq.4a \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"-w+-+3x+%2B+y+-+5z+=+-11\"$ ..............eq.2 , substitute $\"w\"$ and $\"z\"$
\n" ); document.write( " $\"-%2897%2F23+-+%2817%2F23+%29x%29+-+3x+%2B+y+-+5%2840%2F23+-+%2821%2F23%29+x%29+=+-11\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%2853%2F23%29+x%2B+y+-+297%2F23=+-11\"$ ................solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-%2853%2F23%29+x%2B+297%2F23-11\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=+-%2853%2F23%29x%2B44%2F23\"$ ........................eq.5a \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"-4w+-+2x+-+3y+-+z+=+2\"$ ..............eq.4, substitute $\"w\"$ , $\"y\"$ and $\"+z\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

..............solve for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28202+%2F23%29x+-+606%2F23+=+0\"$
\n" ); document.write( " $\"%28202+%2F23%29x+=+606%2F23++\"$
\n" ); document.write( " $\"x=%28606%2F23+%29%2F%28202+%2F23%29\"$
\n" ); document.write( " $\"x=606%2F202\"$
\n" ); document.write( " $\"x=3\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now we can find $\"w\"$ , $\"y\"$ , and $\"+z\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"w=+97%2F23+-+%2817%2F23+%29x\"$ ..........eq.4a , substitute $\"+x\"$
\n" ); document.write( " $\"w=+97%2F23+-+%2817%2F23+%293+\"$
\n" ); document.write( " $\"w=+97%2F23+-+51%2F23\"$
\n" ); document.write( " $\"w=+46%2F23+\"$
\n" ); document.write( " $\"w=+2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=+-+%2853%2F23%29x%2B44%2F23\"$ ........................eq.5a , substitute $\"+x\"$
\n" ); document.write( " $\"y=+-+%28159%2F23%29%2B44%2F23\"$
\n" ); document.write( " $\"y=+-+115%2F23+\"$
\n" ); document.write( " $\"y=-5\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"z=40%2F23+-+%2821%2F23%29x\"$ ..............eq.3a , substitute $\"x\"$
\n" ); document.write( " $\"z=40%2F23+-+%2821%2F23%293\"$
\n" ); document.write( " $\"z=40%2F23+-+%2863%2F23%29\"$
\n" ); document.write( " $\"z=+-%2823%2F23%29\"$
\n" ); document.write( " $\"z=-1\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "solutions:
\n" ); document.write( " $\"x+=+3\"$
\n" ); document.write( " $\"y+=+-5\"$
\n" ); document.write( " $\"w+=+2\"$
\n" ); document.write( " $\"z+=+-1\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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