document.write( "Question 1141157: Solve the following system of equations by using reduction.\r
\n" ); document.write( "\n" ); document.write( "2x + 2y − 2z = 4
\n" ); document.write( "3x + 2y − 2z = −1
\n" ); document.write( "− 4y + 5z = 1 \n" ); document.write( "
Algebra.Com's Answer #761819 by ankor@dixie-net.com(22740)\"\" \"About 
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solve the following system of equations by using reduction.
\n" ); document.write( "2x + 2y − 2z = 4
\n" ); document.write( "3x + 2y − 2z = −1
\n" ); document.write( "− 4y + 5z = 1
\n" ); document.write( ":
\n" ); document.write( "let m represent(2y-2z)
\n" ); document.write( "2x + m = 4
\n" ); document.write( "3x + m = -1
\n" ); document.write( "--------------subtraction elimnates m, find x
\n" ); document.write( "-x = 5
\n" ); document.write( "x = -5
\n" ); document.write( ":
\n" ); document.write( "in the first equation, replace x with -5,
\n" ); document.write( "2(-5) + 2y - 2z = 4
\n" ); document.write( "2y - 2z = 4 + 10
\n" ); document.write( "2y + 2z = 14
\n" ); document.write( "multiply equation by 2 and pair with the 3rd equation
\n" ); document.write( "4y - 4z = 28
\n" ); document.write( "-4y+ 5z = 1
\n" ); document.write( "------------addition eliminates y, find z
\n" ); document.write( "z = 29
\n" ); document.write( "find y using the 3rd equation
\n" ); document.write( "-4y + 5(29) = 11
\n" ); document.write( "-4y + 145 = 11
\n" ); document.write( "-4y = 1 - 145
\n" ); document.write( "-4y = -144
\n" ); document.write( "y = -144/-4
\n" ); document.write( "y = +36
\n" ); document.write( ":
\n" ); document.write( "We then have x=-5, y = 36, z = 29
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution in the 2nd equation
\n" ); document.write( "3x + 2y − 2z = −1
\n" ); document.write( "3(-5) + 2(36) - 2(29) =
\n" ); document.write( "-15 + 72 - 58 = -1
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