document.write( "Question 124016: It states to solve system by graphing. Then it said to idenitfy the system as consistent or inconsistent. Also identify if it is dependent or independent. My question is how do you know when the final answer is consistent, inconsistent, dependent, or independent.
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\n" ); document.write( " 3y=-3x Which the answer would be (2,-2) and again how would I know if it is inconsistent or ect.\r
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Algebra.Com's Answer #90957 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "Discussion
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document.write( "Two variable systems of equations in \"R%5E2\" come in two types:\r
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document.write( "1) Consistent:  There is at least ordered pair in the solution set.
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document.write( "2) Inconsistent:  The solution set is the empty set.\r
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document.write( "Consistent systems are further broken down into two types:
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document.write( "1) Independent:  There is exactly one ordered pair in the solution set.
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document.write( "2) Dependent:  There are an infinite number of ordered pairs in the solution
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document.write( "Graphically, this translates thusly:\r
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document.write( "If the lines have the same slope, they are either parallel or the same line.
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document.write( "Parallel lines represent inconsistent systems.  Two equations that represent
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document.write( "the same line are a dependent consistent system.\r
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document.write( "If the lines have unequal slopes, they represent an independent consistent system.\r
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document.write( "Solution
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document.write( "Your first problem has two equations that are identical if you multiply the
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document.write( "first one by 3.  That means that there are an infinite number of points that
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document.write( "will make either one of the equations a true statement -- you have an infinite
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document.write( "number of points in the solution, so you have a dependent consistent system.\r
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document.write( "Your second problem, if you put your equations into slope-intercept form by
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document.write( "solving each of them for y, you will note that the slope of one line is 1 and
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document.write( "the slope of the other is -1.  Therefore, these lines intersect in exactly
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document.write( "one point and you have an independent consistent system.\r
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document.write( "In general if you have two equations in the form:\r
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document.write( "\"ax%2Bby=c\" and
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document.write( "\"px%2Bqy=r\"\r
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document.write( "If \"a%2Fp=b%2Fq=c%2Fr\" then the system is consistent and dependent (same line,
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document.write( "infinite solutions)\r
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document.write( "If \"a%2Fp=b%2Fq%3C%3Ec%2Fr\" then the system is inconsistent (parallel lines, no
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document.write( "solution)\r
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document.write( "If \"a%2Fp%3C%3Eb%2Fq\" then the system is consistent and independent (one solution)
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