document.write( "Question 918085: Solve the system of equations. If the system has no solution, say it is inconsistent.\r
\n" ); document.write( "\n" ); document.write( "x + y + z = 3
\n" ); document.write( "x - z = 1
\n" ); document.write( "y - z = -4 \n" ); document.write( "

Algebra.Com's Answer #569282 by tommyt3rd(5050) $\"\"$ $\"About$

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Adding (1) and (2) leads to
\n" ); document.write( "(x+y+z)+(x-z)=3+1
\n" ); document.write( "2x+y=4
\n" ); document.write( "(4) y=4-2x \r
\n" ); document.write( "\n" ); document.write( "Adding (1) and (3) leads to
\n" ); document.write( "(x+y+z)+(y-z)=3-4
\n" ); document.write( "x+2y=-1 \r
\n" ); document.write( "\n" ); document.write( "Replacing y with (4) leads to the solution for x:
\n" ); document.write( "x+2(4-2x)=-1
\n" ); document.write( "x+8-4x=-1
\n" ); document.write( "-3x=-9
\n" ); document.write( "x=3\r
\n" ); document.write( "\n" ); document.write( "Using x we can find y:
\n" ); document.write( "y=4-2x=4-2(3)=4-6=-2
\n" ); document.write( "y=-2 \r
\n" ); document.write( "\n" ); document.write( "Next we find z:
\n" ); document.write( "x+y+z=3
\n" ); document.write( "3-2+z=3
\n" ); document.write( "-2+z=0
\n" ); document.write( "z=2 \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "solution: (3, -2, 2) \n" ); document.write( "

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