document.write( "Question 1167063: so Im trying to brush up on my skills and have been presented with: \r
\n" ); document.write( "\n" ); document.write( "x - y - z = 5
\n" ); document.write( "y - x - z = 1
\n" ); document.write( "z - y - x = -15
\n" ); document.write( "x * y - z = a \r
\n" ); document.write( "\n" ); document.write( "so far all I can remember is to equal everything out to zero leaving: \r
\n" ); document.write( "\n" ); document.write( "x - y - z - 5 = 0
\n" ); document.write( "y - x - z - 1 = 0
\n" ); document.write( "z - y - x + 15 = 0
\n" ); document.write( "x * y - z - a = 0\r
\n" ); document.write( "\n" ); document.write( "what kind of problem is this exactly and how do I solve he variables? \n" ); document.write( "

Algebra.Com's Answer #791665 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!
so Im trying to brush up on my skills and have been presented with: \r
\n" ); document.write( "\n" ); document.write( "x - y - z = 5
\n" ); document.write( "y - x - z = 1
\n" ); document.write( "z - y - x = -15
\n" ); document.write( "x * y - z = a \r
\n" ); document.write( "\n" ); document.write( "so far all I can remember is to equal everything out to zero leaving: \r
\n" ); document.write( "\n" ); document.write( "x - y - z - 5 = 0
\n" ); document.write( "y - x - z - 1 = 0
\n" ); document.write( "z - y - x + 15 = 0
\n" ); document.write( "x * y - z - a = 0
\n" ); document.write( "what kind of problem is this exactly and how do I solve he variables?
\n" ); document.write( "

This is a system of equations in 3 VARIABLES. You need to find the value of each of the 3 variables....in this case, x, y, and z. Then determine the value of a, which is: x * y - z.\r\n" );
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document.write( "There're may ways that this system can be solved. The easiest, in my opinion, is the following:\r\n" );
document.write( "x - y - z = 5 -------- eq (i)\r\n" );
document.write( "y - x - z = 1 -------- eq (ii)\r\n" );
document.write( "z - y - x = -15 ------ eq (iii)\r\n" );
document.write( "\r\n" );
document.write( "Rearrange eqs (ii) & (iii) to get: \r\n" );
document.write( "- 2z = 6 ----- Adding eqs (i) & (ii)\r\n" );
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document.write( "- 2x = - 14 ----- Adding eqs (ii) & (iii)\r\n" );
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document.write( "y - 7 - (- 3) = 1 ------ Substituting 7 of x, and - 3 for z in eq (ii)\r\n" );
document.write( "y - 7 + 3 = 1\r\n" );
document.write( "y - 4 = 1\r\n" );
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document.write( "Shouldn't pose a problem now, to find \"a.\"

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