document.write( "Question 305382: Good Morning Algebra.com,
\n" ); document.write( "I have a question for you again and would appreciate your help\r
\n" ); document.write( "\n" ); document.write( "Post a fifty word response to the following\r
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\n" ); document.write( "\n" ); document.write( "o How do you know when an equation has infinitely many solutions?
\n" ); document.write( "o How do you know when an equation has no solution? \r
\n" ); document.write( "\n" ); document.write( "Again Thank you for you help!\r
\n" ); document.write( "\n" ); document.write( "The needy one :) \n" ); document.write( "

Algebra.Com's Answer #218634 by Alan3354(69443) $\"\"$ $\"About$

You can put this solution on YOUR website!
If the number of variables is more than the number of equations, there are an infinite number of solutions.
\n" ); document.write( "x = 6 has one solution.
\n" ); document.write( "x+y = 6 has an infinite number of solutions.
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\n" ); document.write( "You asked about \"an equation\", I think you meant a system of equations.
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\n" ); document.write( "x + y = 2
\n" ); document.write( "x - 2y = 10 has one solution.
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\n" ); document.write( "x + y = 2
\n" ); document.write( "2x + 2y = 4 has an infinite number, the 2nd eqn is 2x the 1st --> dependent.
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\n" ); document.write( "x + y = 2
\n" ); document.write( "x + y = 3 has no solution --> inconsistent.
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\n" ); document.write( "x + y + z = 3
\n" ); document.write( "x + y - z = 1 has an infinite number, only 2 eqns with 3 variables.
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