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graph x+y=-2 and 3x-y=10 using the graphical method
\n" ); document.write( ":
\n" ); document.write( "Arrange the equations into the general (y=) form and plot both graphs
\n" ); document.write( "1st eq:
\n" ); document.write( "x + y = -2
\n" ); document.write( "y = -x - 2
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\n" ); document.write( "2nd eq:
\n" ); document.write( "3x - y = 10
\n" ); document.write( "-y = 10 - 3x
\n" ); document.write( "y = 3x -10; y has to be positive, mult eq by -1
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\n" ); document.write( ":
\n" ); document.write( "1st eq (purple):
\n" ); document.write( "as an example find y when x = -4, substituting for x in; y = x - 2
\n" ); document.write( "y = -(-4) - 2
\n" ); document.write( "y = +4 - 2
\n" ); document.write( "y = 2
\n" ); document.write( "Enter 2 for y in the table, do the same for x=0 and x=+4, you should get:
\n" ); document.write( " x | y
\n" ); document.write( "-------
\n" ); document.write( "-4 |+2
\n" ); document.write( " 0 |-2
\n" ); document.write( "+4 |-6
\n" ); document.write( ":
\n" ); document.write( "2nd eq (green):
\n" ); document.write( "do the same in y = 3x - 10
\n" ); document.write( " x | y
\n" ); document.write( "--------
\n" ); document.write( " -1|-13
\n" ); document.write( " 0|-10
\n" ); document.write( " +4|+2
\n" ); document.write( ":
\n" ); document.write( "Plot this as given, the graph should look this:
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\n" ); document.write( ":
\n" ); document.write( "The solution is the x/y coordinate where the graphs intersect
\n" ); document.write( "You can see this point occurs when x = +2, y = -4
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\n" ); document.write( "You can prove this by substituting 2 for x in both equations and see that
\n" ); document.write( "y = -4 in both equations
\n" ); document.write( ":
\n" ); document.write( "did this help you understand this?\r
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