document.write( "Question 1097060: 1/3x - 3/2y = 4
\n" ); document.write( "2x -by = 20
\n" ); document.write( "in this system of equations b is a constant. If the system has no solution, what is the value of b? \n" ); document.write( "
Algebra.Com's Answer #711493 by ikleyn(52792)\"\" \"About 
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document.write( "This system has no solution in only one case:\r\n" );
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document.write( "     If the coefficients of the second equation are proportional to coefficients of the first equation,\r\n" );
document.write( "     BUT the right hand side terms ARE NOT proportional with that coefficient of proportionality.\r\n" );
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document.write( "     It is the same case when the straight lines of the equations are parallel,\r\n" );
document.write( "     BUT not coincide.\r\n" );
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document.write( "The second equation coefficient \"2\" at \"x\" is 6 times the coefficient 1/3 at \"x\" in the first equation,\r\n" );
document.write( "so the coefficient of proportionality must be 6:  \"%281%2F3%29%2A6\" = 2.\r\n" );
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document.write( "Then \"-3%2F2\" becomes  \"%28-3%2F2%29%2A6\" = -9.\r\n" );
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document.write( "So, \"b\" must be equal 9.\r\n" );
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document.write( "Notice that the right side term 20 IS NOT 6 times 4.\r\n" );
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document.write( "Therefore,  b = 9 is the only value when the system HAS NO solution.\r\n" );
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\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Geometric interpretation of the linear system of two equations in two unknowns \r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Systems of two linear equations in two unknowns\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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