document.write( "Question 24152: I have a math problem I cannot solve can somebody help me PLEASE!\r
\n" ); document.write( "\n" ); document.write( "Determine whether the system has 1 solution,no solution,or many solutions:
\n" ); document.write( "y=-x+2
\n" ); document.write( "3x+3y=6
\n" ); document.write( " and
\n" ); document.write( "y=2/3x
\n" ); document.write( "2x-y=-4 \n" ); document.write( "

Algebra.Com's Answer #12834 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

I have a math problem I cannot solve can somebody help me PLEASE!\r\n" );
document.write( "Determine whether the system has 1 solution,no solution,or many solutions:\r\n" );
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document.write( "First let's define a TOTALLY NUMERICAL EQUATION as an equation \r\n" );
document.write( "that contains no unknowns or variables, just numbers.\r\n" );
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document.write( "Here are some TRUE totally numerical equations:\r\n" );
document.write( "\"2 = 2\", \"-7 = -7\", \"0 = 0\", \"1000 = 1000\"\r\n" );
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document.write( "Here are some FALSE totally numerical equations:\r\n" );
document.write( "\"5 = 3\", \"6 = -8\", \"0 = 1\", \"1000 = 999\"\r\n" );
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document.write( "Rule: \r\n" );
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document.write( "(1) Try to solve either by substitution or by elimination \r\n" );
document.write( "(addition or subtraction). \r\n" );
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document.write( "(2) If you are successful in solving it, then the answer \r\n" );
document.write( "you get is the only solution, and therefore the system has \r\n" );
document.write( "ONE solution.\r\n" );
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document.write( "(3) If you are unable to solve it because it leads to a \r\n" );
document.write( "totally numerical equation, then\r\n" );
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document.write( "(4) If the totally numerical equation is TRUE, the system \r\n" );
document.write( "has MANY solutions.\r\n" );
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document.write( "(5) If the totally numerical equation is FALSE, the system \r\n" );
document.write( "has NO solutions.   \r\n" );
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document.write( " y = -x + 2\r\n" );
document.write( " 3x + 3y = 6\r\n" );
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document.write( "Try to solve by substitution:\r\n" );
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document.write( "Replace y in the second by -x+2 from the first:\r\n" );
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document.write( "3x + 3y = 6\r\n" );
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document.write( "3x + 3(-x + 2) = 6\r\n" );
document.write( "3x - 3x + 6 = 6\r\n" );
document.write( "          6 = 6\r\n" );
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document.write( "This is a totally numerical equation. It is true so there \r\n" );
document.write( "are MANY solutions.\r\n" );
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document.write( "------------------------------------------------------------------\r\n" );
document.write( "and \r\n" );
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document.write( "y=2/3x\r\n" );
document.write( "2x-y=-4\r\n" );
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document.write( "Clear the first one of fractions by multiplying by 3\r\n" );
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document.write( "3y = 2x\r\n" );
document.write( "2x - y = -4\r\n" );
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document.write( "Solve the second equation for y\r\n" );
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document.write( "-y = -4 - 2x\r\n" );
document.write( " y =  4 + 2x\r\n" );
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document.write( "Substitute 4 + 2x for y in the first:\r\n" );
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document.write( "3y = 2x\r\n" );
document.write( "3(4 + 2x) = 2x\r\n" );
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document.write( "12 + 6x = 2x\r\n" );
document.write( "     4x = -12\r\n" );
document.write( "      x = -3\r\n" );
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document.write( "y = 4+2x = 4 + 2(-3) = 4 - 6 = -2\r\n" );
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document.write( "So there is ONE solution  (-3,-2)\r\n" );
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document.write( "----------------------------------------\r\n" );
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document.write( "Here is an example which has NO solutions:\r\n" );
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document.write( " y = -x + 2\r\n" );
document.write( " 3x + 3y = 7\r\n" );
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document.write( "Try to solve by substitution:\r\n" );
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document.write( "Replace y in the second by -x+2 from the first:\r\n" );
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document.write( "3x + 3y = 7\r\n" );
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document.write( "3x + 3(-x + 2) = 7\r\n" );
document.write( "3x - 3x + 6 = 7\r\n" );
document.write( "          6 = 7\r\n" );
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document.write( "This is a totally numerical equation. It is false so there \r\n" );
document.write( "are NO solutions.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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