document.write( "Question 152172: solve the system:\r
\n" ); document.write( "\n" ); document.write( "x+y=4
\n" ); document.write( "x+z=4
\n" ); document.write( "y+z=4 \n" ); document.write( "
Algebra.Com's Answer #111855 by mducky2(62)\"\" \"About 
You can put this solution on YOUR website!
Let's label the equations:
\n" ); document.write( "Equation A: x+y=4
\n" ); document.write( "Equation B: x+z=4
\n" ); document.write( "Equation C: y+z=4
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If we subtract A minus B:
\n" ); document.write( "(x+y) - (x+z) = 4 - 4
\n" ); document.write( "x + y - x - z = 0
\n" ); document.write( "y - z = 0
\n" ); document.write( "y = z
\n" ); document.write( "
If we subtract A minus C:
\n" ); document.write( "(x+y) - (y+z) = 4 - 4
\n" ); document.write( "x + y - y - z = 0
\n" ); document.write( "x - z = 0
\n" ); document.write( "x = z
\n" ); document.write( "
Since y = z and x = z:
\n" ); document.write( "y = x = z
\n" ); document.write( "
Plugging back into Equation A:
\n" ); document.write( "x + x = 4
\n" ); document.write( "2x = 4
\n" ); document.write( "x = 2
\n" ); document.write( "
Since y = x = z:
\n" ); document.write( "y = 2
\n" ); document.write( "z = 2
\n" ); document.write( "
Therefore, y, x, and z all equal 2.\r
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