document.write( "Question 395928: Need help with solving each system by graphing. Appreciate any assistance. Dont understand it at all.\r
\n" ); document.write( "\n" ); document.write( "y = -x + 2
\n" ); document.write( "y = x - 4\r
\n" ); document.write( "\n" ); document.write( "and......\r
\n" ); document.write( "\n" ); document.write( "y= -1/4x - 1
\n" ); document.write( "y= 3/4x + 3
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Algebra.Com's Answer #280962 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!

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\n" ); document.write( "\n" ); document.write( "\"y+=+-x+%2B+2\"
\n" ); document.write( "\"y+=+x+-+4\".........write in standard form\r
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\n" ); document.write( "\n" ); document.write( "\"x+%2B+y+=++2\"\r
\n" ); document.write( "\n" ); document.write( "\"-x+%2B+y+=+-+4\"\r
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Solved by pluggable solver: Solve the System of Equations by Graphing

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\n" ); document.write( " Start with the given system of equations:
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\n" ); document.write( " \"1x%2By=2\"
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\n" ); document.write( " \"-x%2By=-4\"
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\n" ); document.write( " In order to graph these equations, we need to solve for y for each equation.
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\n" ); document.write( " So let's solve for y on the first equation
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\n" ); document.write( " \"1x%2By=2\" Start with the given equation
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\n" ); document.write( " \"1y=2-x\" Subtract \"+x\" from both sides
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\n" ); document.write( " \"1y=-x%2B2\" Rearrange the equation
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\n" ); document.write( " \"y=%28-x%2B2%29%2F%281%29\" Divide both sides by \"1\"
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\n" ); document.write( " \"y=%28-1%2F1%29x%2B%282%29%2F%281%29\" Break up the fraction
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\n" ); document.write( " \"y=-x%2B2\" Reduce
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\n" ); document.write( " Now lets graph \"y=-x%2B2\" (note: if you need help with graphing, check out this solver)
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\n" ); document.write( " \"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B2%29+\" Graph of \"y=-x%2B2\"
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\n" ); document.write( " So let's solve for y on the second equation
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\n" ); document.write( " \"-x%2By=-4\" Start with the given equation
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\n" ); document.write( " \"1y=-4%2Bx\" Add \"+x\" to both sides
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\n" ); document.write( " \"1y=%2Bx-4\" Rearrange the equation
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\n" ); document.write( " \"y=%28%2Bx-4%29%2F%281%29\" Divide both sides by \"1\"
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\n" ); document.write( " \"y=%28%2B1%2F1%29x%2B%28-4%29%2F%281%29\" Break up the fraction
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\n" ); document.write( " \"y=x-4\" Reduce
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\n" ); document.write( " Now lets add the graph of \"y=x-4\" to our first plot to get:
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\n" ); document.write( " \"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B2%2Cx-4%29+\" Graph of \"y=-x%2B2\"(red) and \"y=x-4\"(green)
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\n" ); document.write( " From the graph, we can see that the two lines intersect at the point (\"3\",\"-1\") (note: you might have to adjust the window to see the intersection)

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\n" ); document.write( "\n" ); document.write( "2.\r
\n" ); document.write( "\n" ); document.write( "\"y=+-%281%2F4%29x+-+1\"\r
\n" ); document.write( "\n" ); document.write( "\"y=+%283%2F4%29x+%2B+3\"........write in standard form\r
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\n" ); document.write( "\n" ); document.write( "\"%281%2F4%29x+%2B+y=+-+1\"\r
\n" ); document.write( "\n" ); document.write( "\"-+%283%2F4%29x+%2B+y=+3\"\r
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Solved by pluggable solver: Solve the System of Equations by Graphing

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\n" ); document.write( " Let's look at the first equation \"%281%2F4%29x%2By=-1\"
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\n" ); document.write( " \"4%28%281%2F4%29x%2By%29=4%28-1%29\" Multiply both sides of the first equation by the LCD 4
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\n" ); document.write( " \"1x%2B4y=-4\" Distribute
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\n" ); document.write( " Let's look at the second equation \"%28-3%2F4%29x%2By=3\"
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\n" ); document.write( " \"4%28%28-3%2F4%29x%2By%29=4%283%29\" Multiply both sides of the second equation by the LCD 4
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\n" ); document.write( " \"-3x%2B4y=12\" Distribute
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\n" ); document.write( " So our new system of equations is:
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\n" ); document.write( " \"1x%2B4y=-4\"
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\n" ); document.write( " \"-3x%2B4y=12\"
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\n" ); document.write( " In order to graph these equations, we need to solve for y for each equation.
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\n" ); document.write( " So let's solve for y on the first equation
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\n" ); document.write( "
\n" ); document.write( " \"1x%2B4y=-4\" Start with the given equation
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\n" ); document.write( " \"4y=-4-x\" Subtract \"+x\" from both sides
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\n" ); document.write( " \"4y=-x-4\" Rearrange the equation
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\n" ); document.write( " \"y=%28-x-4%29%2F%284%29\" Divide both sides by \"4\"
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\n" ); document.write( " \"y=%28-1%2F4%29x%2B%28-4%29%2F%284%29\" Break up the fraction
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\n" ); document.write( " \"y=%28-1%2F4%29x-1\" Reduce
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\n" ); document.write( " Now lets graph \"y=%28-1%2F4%29x-1\" (note: if you need help with graphing, check out this solver)
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\n" ); document.write( " \"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F4%29x-1%29+\" Graph of \"y=%28-1%2F4%29x-1\"
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\n" ); document.write( " So let's solve for y on the second equation
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\n" ); document.write( " \"-3x%2B4y=12\" Start with the given equation
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\n" ); document.write( " \"4y=12%2B3x\" Add \"3+x\" to both sides
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\n" ); document.write( " \"4y=%2B3x%2B12\" Rearrange the equation
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\n" ); document.write( " \"y=%28%2B3x%2B12%29%2F%284%29\" Divide both sides by \"4\"
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\n" ); document.write( " \"y=%28%2B3%2F4%29x%2B%2812%29%2F%284%29\" Break up the fraction
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\n" ); document.write( " \"y=%283%2F4%29x%2B3\" Reduce
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\n" ); document.write( " Now lets add the graph of \"y=%283%2F4%29x%2B3\" to our first plot to get:
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\n" ); document.write( " \"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F4%29x-1%2C%283%2F4%29x%2B3%29+\" Graph of \"y=%28-1%2F4%29x-1\"(red) and \"y=%283%2F4%29x%2B3\"(green)
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\n" ); document.write( " From the graph, we can see that the two lines intersect at the point (\"-4\",\"0\") (note: you might have to adjust the window to see the intersection)

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