document.write( "Question 1016896: if x,y,z>= 0, 3y+2z = 3+x, 3y+z = 4-3x, Find the largest and smallest value of 3x-3y+4z. \n" ); document.write( "

Algebra.Com's Answer #633259 by robertb(5830) $\"\"$ $\"About$

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Subtracting the 2nd equation from the 1st equation, and solving for x, we get\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28z%2B1%29%2F4\"$ .\r
\n" ); document.write( "\n" ); document.write( "Now 3 times the 1st equation plus the 2nd equation, and solving for y, we get\r
\n" ); document.write( "\n" ); document.write( " $\"y+=+%2813-7z%29%2F12\"$ .\r
\n" ); document.write( "\n" ); document.write( "Substituting these last two equations into 3x - 3y + 4z, and simplifying, we get
\n" ); document.write( " $\"%2813z+-+5%29%2F2\"$ .\r
\n" ); document.write( "\n" ); document.write( "Since $\"z%3E+=0\"$ , the minimum value of 3x - 3y + 4z is -5/2, while it has no largest value.\r
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