document.write( "Question 316755: solve the system by the substitution method. Can you please show work!\r
\n" ); document.write( "\n" ); document.write( " 2x+y=12
\n" ); document.write( " 3x-y=13 \n" ); document.write( "
Algebra.Com's Answer #226709 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "\"system%282x%2By=12%2C3x-y=13%29\"\r
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\n" ); document.write( "\n" ); document.write( "Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.\r
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\n" ); document.write( "\n" ); document.write( "So let's isolate y in the first equation\r
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\n" ); document.write( "\n" ); document.write( "\"2x%2By=12\" Start with the first equation\r
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\n" ); document.write( "\n" ); document.write( "\"y=12-2x\" Subtract \"2x\" from both sides\r
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\n" ); document.write( "\n" ); document.write( "\"y=-2x%2B12\" Rearrange the equation\r
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\n" ); document.write( "\n" ); document.write( "Since \"y=-2x%2B12\", we can now replace each \"y\" in the second equation with \"-2x%2B12\" to solve for \"x\"\r
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\n" ); document.write( "\n" ); document.write( "\"3x-highlight%28%28-2x%2B12%29%29=13\" Plug in \"y=-2x%2B12\" into the second equation. In other words, replace each \"y\" with \"-2x%2B12\". Notice we've eliminated the \"y\" variables. So we now have a simple equation with one unknown.\r
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\n" ); document.write( "\n" ); document.write( "\"3x%2B2x-12=13\" Distribute the negative\r
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\n" ); document.write( "\n" ); document.write( "\"5x-12=13\" Combine like terms on the left side\r
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\n" ); document.write( "\n" ); document.write( "\"5x=13%2B12\"Add 12 to both sides\r
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\n" ); document.write( "\n" ); document.write( "\"5x=25\" Combine like terms on the right side\r
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\n" ); document.write( "\n" ); document.write( "\"x=%2825%29%2F%285%29\" Divide both sides by 5 to isolate x\r
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\n" ); document.write( "\n" ); document.write( "\"x=5\" Divide\r
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\n" ); document.write( "\n" ); document.write( "-----------------First Answer------------------------------\r
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\n" ); document.write( "\n" ); document.write( "So the first part of our answer is: \"x=5\"\r
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\n" ); document.write( "\n" ); document.write( "Since we know that \"x=5\" we can plug it into the equation \"y=-2x%2B12\" (remember we previously solved for \"y\" in the first equation).\r
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\n" ); document.write( "\n" ); document.write( "\"y=-2x%2B12\" Start with the equation where \"y\" was previously isolated.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-2%285%29%2B12\" Plug in \"x=5\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=-10%2B12\" Multiply\r
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\n" ); document.write( "\n" ); document.write( "\"y=2\" Combine like terms \r
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\n" ); document.write( "\n" ); document.write( "-----------------Second Answer------------------------------\r
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\n" ); document.write( "\n" ); document.write( "So the second part of our answer is: \"y=2\"\r
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\n" ); document.write( "\n" ); document.write( "-----------------Summary------------------------------\r
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\n" ); document.write( "\n" ); document.write( "So our answers are:\r
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\n" ); document.write( "\n" ); document.write( "\"x=5\" and \"y=2\"\r
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\n" ); document.write( "\n" ); document.write( "which form the point \r
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\n" ); document.write( "\n" ); document.write( "Now let's graph the two equations (if you need help with graphing, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( "From the graph, we can see that the two equations intersect at . This visually verifies our answer.\r
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\n" ); document.write( "\n" ); document.write( " graph of \"2x%2By=12\" (red) and \"3x-y=13\" (green) and the intersection of the lines (blue circle).
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