document.write( "Question 1091457: X+Y+Z=4, X+Y-Z=4, 3X+3Y+Z=12
\n" ); document.write( "FIND VARIABLE XYZ \n" ); document.write( "

Algebra.Com's Answer #705878 by greenestamps(13200) $\"\"$ $\"About$

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The first equation says x+y+z is equal to 4; the second says x+y-z is also equal to 4. Either by logical reasoning or by formal algebra, that means z must be 0.

\n" ); document.write( "So now the first two equations both say x+y is 4; and the third says 3x+3y is 12. But that third equation is then equivalent to the other two.

\n" ); document.write( "We know z is 0; and all we know about x and y is that their sum is 4. So we can't find a single solution; there is an infinite family of solutions.
\n" ); document.write( " $\"x%2By+=+4\"$ --> $\"y+=+4-x\"$
\n" ); document.write( "So we can choose any value for x, and then the corresponding y value is 4 minus the x value we chose. Algebraically, there are an infinite set of solutions defined using parameter x as follows:
\n" ); document.write( " $\"x+=+x\"$
\n" ); document.write( " $\"y+=+4-x\"$
\n" ); document.write( " $\"z+=+0\"$ \n" ); document.write( "

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