document.write( "Question 331064: without graphing tell whether the system of equations has a solution or no solution. 3x + y = 10
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Algebra.Com's Answer #237339 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "\"system%283x+%2B+y+=+10%2C%0D%0A12x+%2B+4y+=+15%29\"\r
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document.write( "Rule:  Given the system of equations:\r
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document.write( "\"system%28Ax%2BBy=C%2CDx%2BEy=F%29\"\r
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document.write( "It is one of the three:\r
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document.write( "1.  Independent system: There is exactly 1 solution if \"A%2FD\"\"%22%22%3C%3E%22%22\"\"B%2FE\". \r
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document.write( "(The graph of an independent system consists of two lines intersecting at 1
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document.write( "point.  They have one point in common, which represents the one solution) \r
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document.write( "2.  Dependent system:  There are infinitely many solutions if \"A%2FD\"\"%22%22=%22%22\"\"B%2FE\"\"%22%22=%22%22\"\"C%2FF\".   \r
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document.write( "(The graph  of an dependent system consists of two lines which are one in the
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document.write( "same, that is, they coincide at every point, and their graphs are the same
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document.write( "line. That is, they have every point in common). \r
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document.write( "3.  Inconsistent system:  There are no solutions if \"A%2FD\"\"%22%22=%22%22\"\"B%2FE\"\"%22%22%3C%3E%22%22\"\"C%2FF\".   \r
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document.write( "(The graph  of an inconsistent system consists of two parallel lines, which of
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document.write( "course have no point in common).\r
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document.write( "In your system:\r
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document.write( "\"system%283x+%2B+y+=+10%2C%0D%0A12x+%2B+4y+=+15%29\"\r
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document.write( "A=3, B=1, C=10, D=12, E=4, F=15\r
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document.write( "\"A%2FD=3%2F12=1%2F4\"
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document.write( "\"B%2FE=1%2F4\"
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document.write( "\"C%2FF=10%2F15=2%2F3\"\r
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document.write( "\"A%2FD=1%2F4\"\"%22%22=%22%22\"\"B%2FE=1%2F4\"\"%22%22%3C%3E%22%22\"\"C%2FF=2%2F3\"\r
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document.write( "So yours is an inconsistent system.  (The graph therefore consists of two
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document.write( "parallel lines, which of course have no point in common, as shown below).\r
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