document.write( "Question 200121: -x+4y=-11
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Algebra.Com's Answer #150451 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Start with the given system of equations:\r
\n" ); document.write( "\n" ); document.write( "\"system%28-x%2B4y=-11%2C2x%2B4y=-2%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"2%28-x%2B4y%29=2%28-11%29\" Multiply the both sides of the first equation by 2.\r
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\n" ); document.write( "\n" ); document.write( "\"-2x%2B8y=-22\" Distribute and multiply.\r
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\n" ); document.write( "\n" ); document.write( "So we have the new system of equations:\r
\n" ); document.write( "\n" ); document.write( "\"system%28-2x%2B8y=-22%2C2x%2B4y=-2%29\"\r
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\n" ); document.write( "\n" ); document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r
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\n" ); document.write( "\n" ); document.write( "\"%28-2x%2B8y%29%2B%282x%2B4y%29=%28-22%29%2B%28-2%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28-2x%2B2x%29%2B%288y%2B4y%29=-22%2B-2\" Group like terms.\r
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\n" ); document.write( "\n" ); document.write( "\"0x%2B12y=-24\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "\"12y=-24\" Simplify.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28-24%29%2F%2812%29\" Divide both sides by \"12\" to isolate \"y\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-2\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "\"-2x%2B8y=-22\" Now go back to the first equation.\r
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\n" ); document.write( "\n" ); document.write( "\"-2x%2B8%28-2%29=-22\" Plug in \"y=-2\".\r
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\n" ); document.write( "\n" ); document.write( "\"-2x-16=-22\" Multiply.\r
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\n" ); document.write( "\n" ); document.write( "\"-2x=-22%2B16\" Add \"16\" to both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"-2x=-6\" Combine like terms on the right side.\r
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\n" ); document.write( "\n" ); document.write( "\"x=%28-6%29%2F%28-2%29\" Divide both sides by \"-2\" to isolate \"x\".\r
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\n" ); document.write( "\n" ); document.write( "\"x=3\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So the solutions are \"x=3\" and \"y=-2\".\r
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\n" ); document.write( "\n" ); document.write( "Which form the ordered pair .\r
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\n" ); document.write( "\n" ); document.write( "This means that the system is consistent and independent.\r
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\n" ); document.write( "\n" ); document.write( "Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"-x%2B4y=-11\" (red) and \"2x%2B4y=-2\" (green)
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