document.write( "Question 990674: Consider the system −5x+2y−z = 0 and −5x−2y−z = 0. Both equations
\n" ); document.write( "equal zero and so −5x + 2y − z = −5x − 2y − z which is equivalent to y = 0. Does it follow that x and z can equal anything? Notice that when x = 1, z = −4, and y = 0 are plugged into the equations, the equations do not equal 0. Why? \n" ); document.write( "

Algebra.Com's Answer #610706 by MathTherapy(10557) $\"\"$ $\"About$

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\n" ); document.write( "Consider the system −5x+2y−z = 0 and −5x−2y−z = 0. Both equations
\n" ); document.write( "equal zero and so −5x + 2y − z = −5x − 2y − z which is equivalent to y = 0. Does it follow that x and z can equal anything? Notice that when x = 1, z = −4, and y = 0 are plugged into the equations, the equations do not equal 0. Why?
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y is definitely 0, based on the elimination of the variables, x and z, when one of the equations is subtracted from the other.
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document.write( "One of the variables: x or z can be anything, but the other would be dependent on what that ANYTHING is.
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document.write( "For example, x can be any value, but then z would equal - 5 times that value of x, or .
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document.write( "Likewise, z can be any value, but then x would equal the negative value of z, divided by 5, or  \n" );
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