document.write( "Question 172786: Given the system of equations \r
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\n" ); document.write( "\n" ); document.write( "\"system%28x-4y=-12%2Cy=-4%2B2x%29\"\r
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\n" ); document.write( "\n" ); document.write( "Solve the system of equations by graphing.
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Algebra.Com's Answer #127627 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "First let's graph \"x-4y=-12\". \r
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\n" ); document.write( "\n" ); document.write( "In order to graph \"x-4y=-12\", we need to solve for \"y\"\r
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\n" ); document.write( "\n" ); document.write( "\"x-4y=-12\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"-4y=-12-x\" Subtract \"x\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"-4y=-x-12\" Rearrange the terms.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28-x-12%29%2F%28-4%29\" Divide both sides by \"-4\" to isolate y.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28%28-1%29%2F%28-4%29%29x%2B%28-12%29%2F%28-4%29\" Break up the fraction.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%281%2F4%29x%2B3\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "Looking at \"y=%281%2F4%29x%2B3\" we can see that the equation is in slope-intercept form \"y=mx%2Bb\" where the slope is \"m=1%2F4\" and the y-intercept is \"b=3\" \r
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\n" ); document.write( "\n" ); document.write( "Since \"b=3\" this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis\r
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\n" ); document.write( "\n" ); document.write( "So we have one point \r
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\n" ); document.write( "\n" ); document.write( "Now since the slope is comprised of the \"rise\" over the \"run\" this means\r
\n" ); document.write( "\n" ); document.write( "\"slope=rise%2Frun\"\r
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\n" ); document.write( "\n" ); document.write( "Also, because the slope is \"1%2F4\", this means:\r
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\n" ); document.write( "\n" ); document.write( "\"rise%2Frun=1%2F4\"\r
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\n" ); document.write( "\n" ); document.write( "which shows us that the rise is 1 and the run is 4. This means that to go from point to point, we can go up 1 and over 4\r
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\n" ); document.write( "\n" ); document.write( "So starting at , go up 1 unit \r
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\n" ); document.write( "\n" ); document.write( "and to the right 4 units to get to the next point \r
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\n" ); document.write( "\n" ); document.write( "Now draw a line through these points to graph \"y=%281%2F4%29x%2B3\"\r
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\n" ); document.write( "\n" ); document.write( " So this is the graph of \"y=%281%2F4%29x%2B3\" through the points and \r
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\n" ); document.write( "\n" ); document.write( "Now let's graph \"y=-4%2B2x\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=-4%2B2x\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"y=2x-4\" Rearrange the terms.\r
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\n" ); document.write( "\n" ); document.write( "Looking at \"y=2x-4\" we can see that the equation is in slope-intercept form \"y=mx%2Bb\" where the slope is \"m=2\" and the y-intercept is \"b=-4\" \r
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\n" ); document.write( "\n" ); document.write( "Since \"b=-4\" this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis\r
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\n" ); document.write( "\n" ); document.write( "So we have one point \r
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\n" ); document.write( "\n" ); document.write( "\r
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\n" ); document.write( "\n" ); document.write( "Now since the slope is comprised of the \"rise\" over the \"run\" this means\r
\n" ); document.write( "\n" ); document.write( "\"slope=rise%2Frun\"\r
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\n" ); document.write( "\n" ); document.write( "Also, because the slope is \"2\", this means:\r
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\n" ); document.write( "\n" ); document.write( "\"rise%2Frun=2%2F1\"\r
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\n" ); document.write( "\n" ); document.write( "which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2 and over 1\r
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\n" ); document.write( "\n" ); document.write( "So starting at , go up 2 units \r
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\n" ); document.write( "\n" ); document.write( "and to the right 1 unit to get to the next point \r
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\n" ); document.write( "\n" ); document.write( "Now draw a line through these points to graph \"y=2x-4\"\r
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\n" ); document.write( "\n" ); document.write( " So this is the graph of \"y=2x-4\" through the points and \r
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\n" ); document.write( "\n" ); document.write( "Now let's graph the two equations on the same coordinate system:\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"y=%281%2F4%29x%2B3\" (red) and graph of \"y=2x-4\" (green)\r
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\n" ); document.write( "\n" ); document.write( "From the graph, we can see that the two lines intersect at the point (4,4). So the solution is (4,4)
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