document.write( "Question 1063259: how do I find out with a graph that already has the points plotted if it has no solutions, one, or many? \n" ); document.write( "
Algebra.Com's Answer #678319 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "Let's say you have four points A,B,C,D plotted on the same xy grid. Let's further say that you know A and B lie on the same line. So that means we can draw a line through A and B. Call this line m.\r
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\n" ); document.write( "\n" ); document.write( "If C and D are on the other line, then draw a line through those two points. Call this line n.\r
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\n" ); document.write( "\n" ); document.write( "There are 3 different possible scenarios\r
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\n" ); document.write( "\n" ); document.write( "Scenario 1: Line m and line n cross at exactly 1 point. This is the point of intersection and it is the solution to the system. This system has 1 solution.\r
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\n" ); document.write( "\n" ); document.write( "Scenario 2: The two lines are parallel. This can be visually confirmed or you can determine the slope of each line. The two lines would have equal slopes but different y intercepts if they are parallel. There are no solutions (since the lines never cross)\r
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\n" ); document.write( "\n" ); document.write( "Scenario 3: The two lines are actually one in the same. One line is perfectly right on top of the other line. This means there are infinitely many solutions.
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