document.write( "Question 117044: please help me with this question.I am having difficulty eliminating variables.\r
\n" ); document.write( "\n" ); document.write( "solve the linear system without using matrices or determinants
\n" ); document.write( "x+y+z=2
\n" ); document.write( "x-y+3z=12
\n" ); document.write( "2x+5y+2z=-2 \n" ); document.write( "
Algebra.Com's Answer #85108 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
solve the linear system without using matrices or determinants
\n" ); document.write( "x + y + z = 2
\n" ); document.write( "x - y +3z =12
\n" ); document.write( "2x+5y +2z =-2
\n" ); document.write( ":
\n" ); document.write( "Let's eliminate z, and get it down to two, 2 unknown equations:
\n" ); document.write( "Multiply the 2nd equation by -1 and add all three.
\n" ); document.write( " x + y + z = 2
\n" ); document.write( "-x + y -3z =-12
\n" ); document.write( "2x +5y +2z = -2
\n" ); document.write( "------------------adding eliminate z
\n" ); document.write( "2x +7y +0z = -12
\n" ); document.write( "2x + 7y = -12; our 2 unknown equation
\n" ); document.write( ":
\n" ); document.write( "Here we luck out. Multiply eq1 by -2 and add it to eq3, I should have noticed that at first.
\n" ); document.write( "-2x - 2y - 2z = -4
\n" ); document.write( "2x + 5y + 2z = -2
\n" ); document.write( "--------------------adding eliminates x & z, easy to find y
\n" ); document.write( "0x + 3y + 0z = -6
\n" ); document.write( "3y = -6
\n" ); document.write( "y = -2
\n" ); document.write( ":
\n" ); document.write( "Use our two unknown equation to find x:
\n" ); document.write( "2x + 7y = -12
\n" ); document.write( "Substitute -2 for y
\n" ); document.write( "2x + 7(-2) = -12
\n" ); document.write( "2x -14 = -12
\n" ); document.write( "2x = -12 + 14
\n" ); document.write( "2x = +2
\n" ); document.write( "x = +1
\n" ); document.write( ":
\n" ); document.write( "Use the 1st equation to find z:
\n" ); document.write( "x + y + z = 2
\n" ); document.write( "1 - 2 + z = 2
\n" ); document.write( "z = 2 + 1
\n" ); document.write( "z = +3
\n" ); document.write( ":
\n" ); document.write( "Check our solution the eq 2
\n" ); document.write( "x - y + 3z = 12
\n" ); document.write( "1 -(-2) + 3(3) = 12
\n" ); document.write( "1 + 2 + 9 = 12 confirms our solutions
\n" ); document.write( ":
\n" ); document.write( "It pays to study these systems and see if there is a single operation that will eliminate 2 unknowns at once, otherwise just do what is necessary to get two, 2 unknown equations to work with. Then you can use elimination or substitution quite easily. \r
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