document.write( "Question 329143: solve the system\r
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Algebra.Com's Answer #235979 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Rules for solving a system of three equations in three unknowns:\r\n" );
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document.write( "1. If one of the equations has only two unknowns, call it \"equation 1\".\r\n" );
document.write( "Observe which of the three unknowns is missing from that equation and \r\n" );
document.write( "eliminate that unknown from the other two equations, and call the \r\n" );
document.write( "resulting equation \"equation 2\".\r\n" );
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document.write( "2. If all three equations contain all three unknowns, pick two of the \r\n" );
document.write( "three equations and eliminate an unknown from them, and call the \r\n" );
document.write( "resulting equation \"equation 1\".  Us the eqution you haven't yet used with \r\n" );
document.write( "one of the others and eliminate that same letter.  Call the resulting \r\n" );
document.write( "equation \"equation 2\".\r\n" );
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document.write( "3. Solve the system of two equation in two unknowns, consisting of \"equation\r\n" );
document.write( "1\" and \"equation 2\".\r\n" );
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document.write( "4. Find the third unknown by substituting in one of the original equations \r\n" );
document.write( "that contains that third unknown.\r\n" );
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document.write( "Step 1.  One of the equations has only two unknowns, in fact two of them\r\n" );
document.write( "do.  I'll pick the first one  and call it \"equation 1\"\r\n" );
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document.write( "I observe that the unknown x is missing from \"equation 1\" and \r\n" );
document.write( "so I'll eliminate x from the other two equations:\r\n" );
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document.write( "To eliminate the x's we multiply one of them, say the first, by -1\r\n" );
document.write( "to make the x's cancel when I add them term by term:\r\n" );
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document.write( "Result:\r\n" );
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document.write( ", that's \"equation 2\".\r\n" );
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document.write( "Now we solve the system consisting of equation 1 and equation 2:\r\n" );
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document.write( "Swap the two terms on the left of the first one so the unknowns\r\n" );
document.write( "will be in the same order:\r\n" );
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document.write( "To make the z's cancel when we add them term by term, we multiply the \r\n" );
document.write( "first one through by -1:\r\n" );
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document.write( "Result:\r\n" );
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document.write( "Substitute that in \r\n" );
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document.write( "Substitute those in the original equation  \r\n" );
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document.write( "Solution: \r\n" );
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document.write( "Edwin

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