document.write( "Question 753656: solve step by step to solve linear equation with 3 variables, can you help me solve this step by step please?
\n" ); document.write( "2x-4y-z=17
\n" ); document.write( "x+2y-z=0
\n" ); document.write( "4x-y-z=6 \n" ); document.write( "

Algebra.Com's Answer #458499 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"2x-4y-z=17\"$ ...eq.1
\n" ); document.write( " $\"x%2B2y-z=0\"$ ...eq.2
\n" ); document.write( " $\"4x-y-z=6\"$ ...eq.3
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\n" ); document.write( "\n" ); document.write( " $\"x%2B2y-z=0\"$ ...eq.2..solve for $\"x\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x=z-2y\"$ ...eq.2a.......substitute in .eq.1\r
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\n" ); document.write( "\n" ); document.write( " $\"2%28z-2y%29-4y-z=17\"$ ...eq.1\r
\n" ); document.write( "\n" ); document.write( " $\"2z-4y-4y-z=17\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z-8y=17\"$ ....solve for $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=17%2B8y\"$ ....eq.1a\r
\n" ); document.write( "\n" ); document.write( "go to $\"x=z-2y\"$ ...eq.2a and substitute $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=17%2B8y-2y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=17%2B6y\"$ ........eq.2b\r
\n" ); document.write( "\n" ); document.write( "go to $\"4x-y-z=6\"$ ...eq.3 and substitute $\"z\"$ from eq.1a and $\"x\"$ from eq.2b\r
\n" ); document.write( "\n" ); document.write( " $\"4%2817%2B6y%29-y-%2817%2B8y%29=6\"$ .....solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"68%2B24y-y-17-8y=6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"51%2B24y-9y=6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"15y=6-51\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"15y=-45\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=-45%2F15\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28y=-3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go back to $\"x=17%2B6y\"$ ........eq.2b and find $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=17%2B6%2A%28-3%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=17-18\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28x=-1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go back to $\"z=17%2B8y\"$ ....eq.1a and find $\"z\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=17%2B8%28-3%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"z=17%2B-24\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28z=-7%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "check:\r
\n" ); document.write( "\n" ); document.write( " $\"x%2B2y-z=0\"$ ...eq.2..plug in $\"highlight%28x=-1%29\"$ , $\"highlight%28y=-3%29\"$ , and $\"highlight%28z=-7%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-1%2B2%28-3%29-%28-7%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-1-6%2B7=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-7%2B7=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=0\"$ which confirms our solutions\r
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