document.write( "Question 1105478: determine the value of p and q for which (–4,–3) will be solution of the system {px+qy=–26 {qx–py =7 \n" ); document.write( "

Algebra.Com's Answer #720340 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "The condition says:  substitute x= -4  and  y= -3  into the given system; then solve it for \"p\" and \"q\".\r\n" );
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document.write( "When you substitute, you will get\r\n" );
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document.write( "-4p -    3q = -26,\r\n" );
document.write( "-4q - (-3)p =   7,\r\n" );
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document.write( "or, equivalently,\r\n" );
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document.write( "4p + 3q = 26,      (1)\r\n" );
document.write( "3p - 4q =  7.      (2)\r\n" );
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document.write( "To solve it, multiply eq(1) by 3 (both sides) and nultiply eq(2) by 4 (both sides).  You will get\r\n" );
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document.write( "12p +  9q = 78,\r\n" );
document.write( "12p - 16q = 28.\r\n" );
document.write( "------------------------Now subtract eq(4) from eq(3)  (both sides). You will get\r\n" );
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document.write( "      25q = 78 - 28 = 50  ====>  q =  = 2.\r\n" );
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document.write( "Then from (2)  3p = 7 + 4q = 7 + 4*2 = 15  ====>  p =  = 5.\r\n" );
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document.write( "Answer.  p = 5,  q = 2.\r\n" );
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