document.write( "Question 804413: Can you pretty please with a cherry on top help me with this. Im terribly confused. Thank you (:\r
\n" ); document.write( "\n" ); document.write( "2x - y + z = 7
\n" ); document.write( "x + 2y + 2z = 3
\n" ); document.write( "7x - 3y - 3z = 4 \n" ); document.write( "

Algebra.Com's Answer #484734 by erica65404(394) $\"\"$ $\"About$

You can put this solution on YOUR website!
Equation A: $\"2x-y%2Bz=7\"$
\n" ); document.write( "Equation B: $\"x%2B2y%2B2z=3\"$
\n" ); document.write( "Equation C: $\"7x-3y-3z=4\"$
\n" ); document.write( "For these kind of problems, you need to start by eliminating either x, y, or z.
\n" ); document.write( "We are going to start with x.
\n" ); document.write( "Take 2 of the 3 given equations.
\n" ); document.write( "I am going to use Equation A and B.
\n" ); document.write( " $\"2x-y%2Bz=7\"$
\n" ); document.write( " $\"x%2B2y%2B2z=3\"$
\n" ); document.write( "you want the x's to be opposites.
\n" ); document.write( "To do so we are going to multiply equation B by -2.
\n" ); document.write( " $\"-2%28x%2B2y%2B2z%29=-2%283%29\"$
\n" ); document.write( " $\"-2x-4y-4z=-6\"$
\n" ); document.write( "now you add the two equations together.
\n" ); document.write( " $\"2x-y%2Bz=7\"$
\n" ); document.write( "+
\n" ); document.write( " $\"-2x-4y-4z=-6\"$
\n" ); document.write( " $\"-5y-3z=1\"$
\n" ); document.write( "Now lets take equation B and C and eliminate x again.
\n" ); document.write( " $\"x%2B2y%2B2z=3\"$
\n" ); document.write( " $\"7x-3y-3z=4\"$
\n" ); document.write( "we will multiply equation B by -7.
\n" ); document.write( " $\"-7%28x%2B2y%2B2z%29=-7%283%29\"$
\n" ); document.write( " $\"-7x-14y-14z-21\"$
\n" ); document.write( "add the two equations together
\n" ); document.write( " $\"-7x-14y-14z-21\"$
\n" ); document.write( "+
\n" ); document.write( " $\"7x-3y-3z=4\"$
\n" ); document.write( " $\"-17y-17z=-17\"$
\n" ); document.write( "you can divide the equation by-17
\n" ); document.write( " $\"%28-17y-17z%29%2F-17=-17%2F-17\"$
\n" ); document.write( " $\"y%2Bz=1\"$
\n" ); document.write( "We now have two equations with only y and z.
\n" ); document.write( " $\"-5y-3z=1\"$
\n" ); document.write( " $\"y%2Bz=1\"$
\n" ); document.write( "We will now eliminate z
\n" ); document.write( "multiply $\"y%2Bz=1\"$ by 3
\n" ); document.write( " $\"3y%2B3z=3\"$
\n" ); document.write( "add the two equations.
\n" ); document.write( " $\"-5y-3z=1\"$
\n" ); document.write( "+
\n" ); document.write( " $\"3y%2B3z=3\"$
\n" ); document.write( " $\"-2y=4\"$
\n" ); document.write( " $\"y=-2\"$
\n" ); document.write( "plug y=-2 into $\"y%2Bz=1\"$
\n" ); document.write( " $\"-2%2Bz=1\"$
\n" ); document.write( " $\"z=3\"$
\n" ); document.write( "Now plug y=-2 and z=3 into equation A.
\n" ); document.write( " $\"2x-2%2B3=7\"$
\n" ); document.write( " $\"2x=6\"$
\n" ); document.write( " $\"x=3\"$
\n" ); document.write( "the answer is x=3, y=-2, and z=3. \n" ); document.write( "

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