document.write( "Question 908468: 2x+3y=-5
\n" ); document.write( "4y-5z=-32
\n" ); document.write( "3x+2z=14
\n" ); document.write( "Please show me how to solve for X, Y , and Z using substitution. Thank You \n" ); document.write( "
Algebra.Com's Answer #551077 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Substitution isn't the easiest way. Elimination is easier,\r\n" );
document.write( "But you specified substitution, so here goes:\r\n" );
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document.write( "(1)  \"2x%2B3y=-5\"\r\n" );
document.write( "(2)  \"4y-5z=-32\"\r\n" );
document.write( "(3)  \"3x%2B2z=14\"\r\n" );
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document.write( "Pick any equation and solve for any letter:\r\n" );
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document.write( "I'll arbitrarily pick equation 2 and arbitrarily solve for y\r\n" );
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document.write( "\"4y-5z=-32\"\r\n" );
document.write( "\"4y=5z-32\"\r\n" );
document.write( "(4)  \"y=%285z-32%29%2F4\"\r\n" );
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document.write( "Substitute for y in (1)\r\n" );
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document.write( "(1)  \"2x%2B3y=-5\"\r\n" );
document.write( "     \"2x%2B3%28%285z-32%29%2F4%29=-5\"\r\n" );
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document.write( "Multiply through by 4 to clear the fraction:\r\n" );
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document.write( "     \"8x%2B3%285z-32%29=-20\"\r\n" );
document.write( "     \"8x%2B15z-96=-20\"\r\n" );
document.write( "(5)  \"8x%2B15z=76\"\r\n" );
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document.write( "We notice that (3) contains the same letters as (5)\r\n" );
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document.write( "Solve (3) for one of its letters.\r\n" );
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document.write( "I'll arbitrarily solve (3) for z\r\n" );
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document.write( "(3)  \"3x%2B2z=14\"\r\n" );
document.write( "     \"2z=14-3x\"\r\n" );
document.write( "(6)  \"z=%2814-3x%29%2F2\"\r\n" );
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document.write( "Substitute in (5)\r\n" );
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document.write( "(5)   \"8x%2B15z=76\"\r\n" );
document.write( "      \"8x%2B15%2814-3x%29%2F2=76\"\r\n" );
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document.write( "Multiply by 2 to clear the fraction:\r\n" );
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document.write( "      \"16x%2B15%2814-3x%29=152\"\r\n" );
document.write( "      \"16x%2B210-45x=152\"\r\n" );
document.write( "      \"-29x%2B210=152\"\r\n" );
document.write( "      \"-29x=-58\"\r\n" );
document.write( "      \"x=%28-58%29%2F%28-29%29\"\r\n" );
document.write( "      \"x=2\"\r\n" );
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document.write( "Substitute in (6)\r\n" );
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document.write( "(6)  \"z=%2814-3x%29%2F2\"\r\n" );
document.write( "     \"z=%2814-3%282%29%29%2F2\"\r\n" );
document.write( "     \"z=%2814-6%29%2F2\"\r\n" );
document.write( "     \"z=8%2F2\"\r\n" );
document.write( "     \"z=4\"\r\n" );
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document.write( "(4)  \"y=%285z-32%29%2F4\"  \r\n" );
document.write( "     \"y=%285%284%29-32%29%2F4\"\r\n" );
document.write( "     \"y=%2820-32%29%2F4\"\r\n" );
document.write( "     \"y=%28-12%29%2F4\"\r\n" );
document.write( "     \"y=-3\"   \r\n" );
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document.write( "(x,y,z) = (2,-3,4)\r\n" );
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document.write( "Edwin
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