document.write( "Question 729957: How to do the System of equations. It says solve the system of equations\r
\n" ); document.write( "\n" ); document.write( "a) 2x+3y+7z=13 b) x+3y+5z=20
\n" ); document.write( " 3x+2y-5z=-22 y-4z=-16
\n" ); document.write( " 5x+7y-3z=-28 3x+2y+9z=36
\n" ); document.write( "

Algebra.Com's Answer #446340 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
a) \r
\n" ); document.write( "\n" ); document.write( "\"2x%2B3y%2B7z=13\"........eq. 1
\n" ); document.write( "\"3x%2B2y-5z=-22\"........eq. 2
\n" ); document.write( "\"5x%2B7y-3z=-28\"........eq. 3
\n" ); document.write( "________________________\r
\n" ); document.write( "\n" ); document.write( "\"2x%2B3y%2B7z=13\"........eq. 1 ..both multiply: eq1 by 3, eq 2 by 2
\n" ); document.write( "\"3x%2B2y-5z=-22\"........eq. 2 \r
\n" ); document.write( "\n" ); document.write( "\"6x%2B9y%2B21z=39\"........eq. 1
\n" ); document.write( "\"6x%2B4y-10z=-44\"........eq. 2 .......subtract
\n" ); document.write( "______________________ \r
\n" ); document.write( "\n" ); document.write( "\"6x%2B9y%2B21z-%286x%2B4y-10z%29=39-%28-44%29\"\r
\n" ); document.write( "\n" ); document.write( "\"6x%2B9y%2B21z-6x-4y%2B10z=39%2B44\"\r
\n" ); document.write( "\n" ); document.write( "\"5y%2B31z=83\"......eq. 1a\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"3x%2B2y-5z=-22\"........eq. 2 ...both multiply: eq2 by 5, eq 3 by 3
\n" ); document.write( "\"5x%2B7y-3z=-28\"........eq. 3
\n" ); document.write( "________________________\r
\n" ); document.write( "\n" ); document.write( "\"15x%2B10y-25z=-110\"........eq. 2
\n" ); document.write( "\"15x%2B21y-9z=-84\"........eq. 3
\n" ); document.write( "________________________.......subtract\r
\n" ); document.write( "\n" ); document.write( "\"15x%2B10y-25z-%2815x%2B21y-9z%29=-110-%28-84%29\"\r
\n" ); document.write( "\n" ); document.write( "\"15x%2B10y-25z-15x-21y%2B9z%29=-110%2B84\"\r
\n" ); document.write( "\n" ); document.write( "\"-11y-16z=-26\"......eq. 2a\r
\n" ); document.write( "\n" ); document.write( "take eq. 1a and 2a\r
\n" ); document.write( "\n" ); document.write( "\"5y%2B31z=83\"......eq. 1a....both multiply: eq1a by 11, eq 2a by 5\r
\n" ); document.write( "\n" ); document.write( "\"-11y-16z=-26\"......eq. 2a
\n" ); document.write( "_____________________________\r
\n" ); document.write( "\n" ); document.write( "\"55y%2B341z=913\"......eq. 1a.
\n" ); document.write( "\"-55y-80z=-130\"......eq. 2a
\n" ); document.write( "_____________________________...add\r
\n" ); document.write( "\n" ); document.write( "\"55y%2B341z%2B%28-55y-80z%29=913%2B%28-130%29\"
\n" ); document.write( "\"55y%2B341z-55y-80z=913-130\"\r
\n" ); document.write( "\n" ); document.write( "\"341z-80z=783\"\r
\n" ); document.write( "\n" ); document.write( "\"261z=783\"\r
\n" ); document.write( "\n" ); document.write( "\"z=783%2F261\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28z=3%29\"\r
\n" ); document.write( "\n" ); document.write( "now go back to \"55y%2B341z=913\"......eq. 1a., plug in \"z\" and solve for \"y\"\r
\n" ); document.write( "\n" ); document.write( "\"55y%2B341%2A3=913\"\r
\n" ); document.write( "\n" ); document.write( "\"55y%2B1023=913\"\r
\n" ); document.write( "\n" ); document.write( "\"55y=913-1023\"
\n" ); document.write( "\"55y=-110\"
\n" ); document.write( "\"y=-110%2F55\"
\n" ); document.write( "\"highlight%28y=-2%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now go back to \"2x%2B3y%2B7z=13\"........eq. 1., plug in \"y\" and \"z\" and solve for \"x\"\r
\n" ); document.write( "\n" ); document.write( "\"2x%2B3%28-2%29%2B7%2A3=13\"........eq. 1\r
\n" ); document.write( "\n" ); document.write( "\"2x-6%2B21=13\"\r
\n" ); document.write( "\n" ); document.write( "\"2x%2B15=13\"\r
\n" ); document.write( "\n" ); document.write( "\"2x=13-15\"\r
\n" ); document.write( "\n" ); document.write( "\"2x=-2\"\r
\n" ); document.write( "\n" ); document.write( "\"x=-2%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28x=-1%29\"\r
\n" ); document.write( "
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\n" ); document.write( "\n" ); document.write( "b)
\n" ); document.write( "\"x%2B3y%2B5z=20\"........eq. 1
\n" ); document.write( "\"y-4z=-16\".............eq. 2
\n" ); document.write( "\"3x%2B2y%2B9z=36\"........eq. 3
\n" ); document.write( "________________________\r
\n" ); document.write( "\n" ); document.write( "\"3x%2B9y%2B15z=60\"........eq. 1 ..multiply: eq1 by 3,
\n" ); document.write( "\"3x%2B2y%2B9z=36\"........eq. 3 ...subtract
\n" ); document.write( "______________________ \r
\n" ); document.write( "\n" ); document.write( "\"3x%2B9y%2B15z-%283x%2B2y%2B9z%29=60-36\"
\n" ); document.write( "\"3x%2B9y%2B15z-3x-2y-9z=24\"
\n" ); document.write( "\"7y%2B6z=24\".........................eq. 1a\r
\n" ); document.write( "\n" ); document.write( "take
\n" ); document.write( "\"7y%2B6z=24\".........................eq. 1a
\n" ); document.write( "\"y-4z=-16\".............eq. 2 ............multiply by \"7\" and subtract
\n" ); document.write( "______________________________\r
\n" ); document.write( "\n" ); document.write( "\"7y%2B6z=24\".........................eq. 1a
\n" ); document.write( "\"7y-28z=-112\".............eq. 2
\n" ); document.write( "____________________________subtract
\n" ); document.write( "\"7y%2B6z-%287y-28z%29=24-%28-112%29\"\r
\n" ); document.write( "\n" ); document.write( "\"7y%2B6z-7y%2B28z=24%2B112\"\r
\n" ); document.write( "\n" ); document.write( "\"34z=136\"\r
\n" ); document.write( "\n" ); document.write( "\"z=136%2F34\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28z=4%29\"\r
\n" ); document.write( "\n" ); document.write( "go back to\r
\n" ); document.write( "\n" ); document.write( "\"y-4z=-16\".............eq. 2 , plug in \"z\" and solve for \"y\"\r
\n" ); document.write( "\n" ); document.write( "\"y-4%2A4=-16\"\r
\n" ); document.write( "\n" ); document.write( "\"y-16=-16\"\r
\n" ); document.write( "\n" ); document.write( "\"y=-16%2B16\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28y=0%29\"\r
\n" ); document.write( "\n" ); document.write( "go to \"x%2B3y%2B5z=20\"........eq. 1 plug in \"y\" and \"z\" and solve for \"x\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x%2B3%2A0%2B5%2A4=20\".\r
\n" ); document.write( "\n" ); document.write( "\"x%2B0%2B20=20\"\r
\n" ); document.write( "\n" ); document.write( "\"x=20-20\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28x=0%29\"\r
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