document.write( "Question 1038576: in the system of equations below, u and v are constants. If the system has more than one solution, what is the value of u/v?\r
\n" ); document.write( "\n" ); document.write( " -2x + uy = v
\n" ); document.write( " x-2y = 3 \n" ); document.write( "

Algebra.Com's Answer #653472 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "in the system of equations below, u and v are constants. If the system has more than one solution, what is the value of u/v?\r
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document.write( "-2x + uy = v,      (1)\r\n" );
document.write( "  x - 2y = 3.      (2)\r\n" );
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document.write( "Multiply equation (2) by -2. You will get an equivalent system\r\n" );
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document.write( "-2x + uy =  v,     (1')\r\n" );
document.write( "-2x + 4y = -6.     (2')\r\n" );
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document.write( "The system (1'), (2') has more than one solution if and only if \r\n" );
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document.write( "  u = 4  and  v = -6.\r\n" );
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document.write( "Why it is so?  -  Read the lesson Geometric interpretation of the linear system of two equations in two unknowns in this site.\r\n" );
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