document.write( "Question 1052415: solve each system of equations by using the substitution method.\r
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Algebra.Com's Answer #667777 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Instead of doing yours for you, I will change the numbers,\r\n" );
document.write( "do it step by step.  Then you can use it as a model to do \r\n" );
document.write( "yours exactly the same way step by step:\r\n" );
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\n" ); document.write( "4x + 5y = 21
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document.write( "Write \r\n" );
document.write( "4x + 5y = 21\r\n" );
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document.write( "Take out the y and put in (-3x + 4) in place of it\r\n" );
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document.write( "4x + 5(-3x + 4) = 21\r\n" );
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document.write( "Remove the parentheses by distributing the \"+ 5\" times\r\n" );
document.write( "the \"-3x\", getting \"- 15x\" and also multiplying the \"+ 5\"\r\n" );
document.write( "times the \"+ 4\" getting \"+ 20\", so write \"- 15x + 20\"\r\n" );
document.write( "in place of + 5(-3x + 4)\r\n" );
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document.write( "4x - 15x + 20 = 21\r\n" );
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document.write( "Combine the \"4x - 15x\" as -11x, so write -11x instead of \r\n" );
document.write( "\"4x - 15x\":\r\n" );
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document.write( "    -11x + 20 = 21\r\n" );
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document.write( "Add - 20 to both sides:\r\n" );
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document.write( " -11x + 20 - 20 = 21 - 20\r\n" );
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document.write( "The + 20 and the - 20 cancel out on the left,\r\n" );
document.write( "so we just have -11x on the left. On the right\r\n" );
document.write( "we replace the 21 - 20 by 1\r\n" );
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document.write( "          -11x = 1\r\n" );
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document.write( "We divide both sides by -11\r\n" );
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document.write( "         \"%28-11x%29%2F%28-11%29\"\"%22%22=%22%22\"\"1%2F%28-11%29\"\r\n" );
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document.write( "Then the -11's cancel, and the right side becomes \"-1%2F11\".\r\n" );
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document.write( "So that means \r\n" );
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document.write( "         \"x\"\"%22%22=%22%22\"\"-1%2F11\"\r\n" );
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document.write( "Now we take the original second equation:\r\n" );
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document.write( "         y = -3x + 4\r\n" );
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document.write( "And we substitute \"%28-1%2F11%29\" for x\r\n" );
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document.write( "         y = -3\"%28-1%2F11%29\" + 4\r\n" );
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document.write( "Multiply the -3 by the \"%28-1%2F11%29\", getting \"3%2F11\"\r\n" );
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document.write( "         y = \"3%2F11\" + 4\r\n" );
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document.write( "Get the least common denominator which is 11 by multiplying\r\n" );
document.write( "the +4 by \"%2811%2F11%29\" which just amounts to multiplying by 1:\r\n" );
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document.write( "         y = \"3%2F11\" + 4\"%2811%2F11%29\"\r\n" );
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document.write( "So we have\r\n" );
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document.write( "         y = \"3%2F11\" + \"44%2F11\"\r\n" );
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document.write( "or\r\n" );
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document.write( "         y = \"47%2F11\"\r\n" );
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document.write( "So the solution is (x,y) = \"%28matrix%281%2C3%2C-1%2F11%2C%22%2C%22%2C47%2F11%29%29\"\r\n" );
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document.write( "Now do yours exactly the same way.\r\n" );
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document.write( "Edwin
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