document.write( "Question 158543: Solve the system by graphing.
\n" ); document.write( "3x-2y=4
\n" ); document.write( "-6x+4y=7
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Algebra.Com's Answer #116811 by Electrified_Levi(103)\"\" \"About 
You can put this solution on YOUR website!
Hi, Hope I can help
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\n" ); document.write( "Solve the system by graphing.
\n" ); document.write( "\"+3x-2y=4+\"
\n" ); document.write( "\"+-6x%2B4y=7+\"
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\n" ); document.write( "Points are given as (x,y), to find points on both of these lines, you just replace \"x\" with any number and solve for \"y\"
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\n" ); document.write( "Lets find some points on the first line
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\n" ); document.write( "\"+3x-2y=4+\", (we can use any number for \"x\", then we solve for \"y\"
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\n" ); document.write( "Lets replace \"x\" with \"2\", \"+3x-2y=4+\" = \"+3%282%29-2y=4+\" = \"+6+-2y=4+\"
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\n" ); document.write( "We will move (-2y) over to the right side
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\n" ); document.write( "\"+6+-2y=4+\" = \"+6+-2y+%2B+2y=4+%2B+2y+\" = \"+6+=+4+%2B+2y+\", we will move \"4\" to the left side
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\n" ); document.write( "\"+6+=+4+%2B+2y+\" = \"+6+-+4+=+4+-+4+%2B+2y+\" = \"+2+=++2y+\" = \"+2y+=++2+\"
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\n" ); document.write( "To get \"y\", we will divide each side by \"2\"
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\n" ); document.write( "\"+2y+=++2+\" = \"+2y%2F2+=++2%2F2+\" = \"+y+=++1+\",
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\n" ); document.write( "\"x\" = 2
\n" ); document.write( "\"y\" = 1
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\n" ); document.write( "Since points are given as (x,y), this point would be (2,1)
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\n" ); document.write( "(2,1) is a point of the line(We can check by replacing \"x\" with \"2\", \"y\" with \"1\", \"+3x-2y=4+\" = \"+3%282%29-2%281%29=4+\" = \"+6-2=4+\" = \"+4=4+\" (True)
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\n" ); document.write( "Lets find another point,
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\n" ); document.write( "Lets replace \"x\" with \"0\"
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\n" ); document.write( "\"+3x-2y=4+\" = \"+3%280%29-2y=4+\" = \"+0-2y=4+\" = \"+%28-2y%29=4+\"
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\n" ); document.write( "We can multiply each side by (-1) to get (-2y) positive
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\n" ); document.write( "\"+%28-2y%29=4+\" = \"+%28-2y%29%28-1%29=4%28-1%29+\" = \"+2y+=+%28-4%29+\", to find \"y\" we will divide each side by \"2\"
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\n" ); document.write( "\"+2y+=+%28-4%29+\" = \"+2y%2F2+=+%28-4%29%2F2+\" = \"+y+=+%28-2%29+\"
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\n" ); document.write( "\"x\" = 0
\n" ); document.write( "\"y\" = (-2)
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\n" ); document.write( "Another point on the line is (0,-2)(x,y)(we can check by replacing \"x\" with \"0\", \"y\" with (-2), \"+3x-2y=4+\" = \"+3%280%29-2%28-2%29=4+\" = \"+0%2B4=4+\" = \"+4+=+4+\" (True)
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\n" ); document.write( "Another point on the line is (-4,-8), We can check by replacing \"x\" with (-4), \"y\" with (-8), \"+3x-2y=4+\" = \"+3%28-4%29-2%28-8%29=4+\" = \"+%28-12%29%2B16=4+\" = \"+4+=+4+\" (True)
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\n" ); document.write( "Lets draw a line through the points,
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\n" ); document.write( "Now lets find some points for the second equation, \"+-6x%2B4y=7+\"
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\n" ); document.write( "Lets replace \"x\" with \"+-1%2F2+\", \"+-6x%2B4y=7+\" = \"+-6%28-1%2F2%29%2B4y=7+\" = \"+3%2B4y=7+\"
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\n" ); document.write( "\"4y\" has to equal \"4\", so \"+4y+=+4+\", divide each side by \"4\", \"+4y+=+4+\" = \"+4y%2F4+=+4%2F4+\" = \"+y+=+1+\"
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\n" ); document.write( "x = \"+-1%2F2+\"
\n" ); document.write( "y = 1
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\n" ); document.write( "One point on the line is (\"+-1%2F2\",1 )(We can check by replacing \"x\" with \"+-1%2F2\",\"y\" with \"1\", \"+-6x%2B4y=7+\" = \"+-6%28-1%2F2%29%2B4%281%29=7+\" = \"+3+%2B+4+=+7+\" = \"+7+=+7+\" (True)
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\n" ); document.write( "Replace \"x\" with \"4\", \"+-6x%2B4y=7+\" = \"+-6%284%29%2B4y=7+\" = \"+%28-24%29%2B4y=7+\"
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\n" ); document.write( "\"4y\" will have to equal \"31\", \"+4y+=+31+\", dividing each side by \"4\" will get \"y\"
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\n" ); document.write( "\"+4y+=+31+\" = \"+4y%2F4+=+31%2F4+\" = \"+y+=+31%2F4+\"
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\n" ); document.write( "x = 4
\n" ); document.write( "y = \"+31%2F4+\", or 7 \"+3%2F4+\"
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\n" ); document.write( "The point is (4,\"31%2F4\"), (we can check by replacing \"x\" with \"4\", \"y\" with \"+31%2F4+\", \"+-6x%2B4y=7+\" = \"+-6%284%29%2B4%2831%2F4%29=7+\" = \"+%28-24%29%2B31+=+7+\" = \"+7+=7+\" (True)
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\n" ); document.write( "Another point on the line is ( 0, \"+7%2F4+\" ), ( we can check by replacing \"x\" with \"0\", \"y\" with \"\"+7%2F4+\"\", \"+-6x%2B4y=7+\" = \"+-6%280%29%2B4%287%2F4%29=7+\" = \"+0+%2B+7+=7+\" = \"+7+=+7+\" (True)
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\n" ); document.write( "Lets draw a line through the points
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\n" ); document.write( "These lines are parallel, they don't have any points that intersect each other, there is no solution to the system of equations
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\n" ); document.write( "Hope I helped, Levi
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