document.write( "Question 394281: Use the substitution method to solve the linear system.\r
\n" ); document.write( "\n" ); document.write( "y = x - 4
\n" ); document.write( "3x - y = -8\r
\n" ); document.write( "\n" ); document.write( "I need help graphing the equations.\r
\n" ); document.write( "\n" ); document.write( "Thank you,
\n" ); document.write( "Shannon \n" ); document.write( "
Algebra.Com's Answer #279758 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "\"y+=+x+-+4\"...write in standard form\r
\n" ); document.write( "\n" ); document.write( "\"3x+-+y+=+-8\"\r
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\n" ); document.write( "\n" ); document.write( "\"-x+%2B+y+=++-+4\"\r
\n" ); document.write( "\n" ); document.write( "\"3x+-+y+=+-8\"\r
\n" ); document.write( "\n" ); document.write( "--------------------\r
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Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
\n" ); document.write( " \"+system%28+%0D%0A++++-1%5Cx+%2B+1%5Cy+=+-4%2C%0D%0A++++3%5Cx+%2B+-1%5Cy+=+-8+%29%0D%0A++\"We'll use substitution. After moving 1*y to the right, we get:
\n" ); document.write( " \"-1%2Ax+=+-4+-+1%2Ay\", or \"x+=+-4%2F-1+-+1%2Ay%2F-1\". Substitute that
\n" ); document.write( " into another equation:
\n" ); document.write( " \"3%2A%28-4%2F-1+-+1%2Ay%2F-1%29+%2B+-1%5Cy+=+-8\" and simplify: So, we know that y=-10. Since \"x+=+-4%2F-1+-+1%2Ay%2F-1\", x=-6.
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\n" ); document.write( " Answer: \"system%28+x=-6%2C+y=-10+%29\".
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\n" ); document.write( "\n" ); document.write( "now graph:\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( " \"-x%2By=-4\"
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\n" ); document.write( " \"3x-y=-8\"
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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( " \"-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 graph \"y=x-4\" (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-4%29+\" Graph of \"y=x-4\"
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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-y=-8\" Start with the given equation
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\n" ); document.write( " \"-y=-8-3x\" Subtract \"3+x\" from both sides
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\n" ); document.write( " \"-y=-3x-8\" Rearrange the equation
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\n" ); document.write( " \"y=%28-3x-8%29%2F%28-1%29\" Divide both sides by \"-1\"
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\n" ); document.write( " \"y=%28-3%2F-1%29x%2B%28-8%29%2F%28-1%29\" Break up the fraction
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\n" ); document.write( " \"y=3x%2B8\" Reduce
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\n" ); document.write( " Now lets add the graph of \"y=3x%2B8\" 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-4%2C3x%2B8%29+\" Graph of \"y=x-4\"(red) and \"y=3x%2B8\"(green)
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\n" ); document.write( " From the graph, we can see that the two lines intersect at the point (\"-6\",\"-10\") (note: you might have to adjust the window to see the intersection)

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