document.write( "Question 1208192: 3a+5b=3,a+2b=13
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Algebra.Com's Answer #846437 by ikleyn(52788) $\"\"$ $\"About$

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3a+5b=3, a+2b=13
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document.write( "They want you solve this system of two equations\r\n" );
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document.write( "    3a + 5b =  3,     (1)\r\n" );
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document.write( "     a + 2b = 13.     (2)\r\n" );
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document.write( "There are different methods for it.\r\n" );
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document.write( "I will show here the SUBSTITUTION method.\r\n" );
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document.write( "From equation (2), express  a = 13 - 2b.  \r\n" );
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document.write( "Substitute this expression for \"a\" into equation (1).  You will get\r\n" );
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document.write( "    3*(13-2b) + 5b = 3.\r\n" );
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document.write( "It is a single equation for a single unknown \"b\". \r\n" );
document.write( "Simplify it and find  \"b\"\r\n" );
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document.write( "    39 - 6b + 5b = 3,\r\n" );
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document.write( "    39 - b = 3,\r\n" );
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document.write( "    39 - 3 = b,\r\n" );
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document.write( "    b   = 36.\r\n" );
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document.write( "Substitute this value b = 36 into equation (2) and find \"a\"\r\n" );
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document.write( "    a + 2*36 = 13,\r\n" );
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document.write( "    a + 72 = 13,\r\n" );
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document.write( "    a = 13 - 72 = -59.\r\n" );
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document.write( "Thus a= -59, b= 36 is the unique solution to the original system.    ANSWER \r\n" );
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document.write( "You may check that each equation (1) and (2) becomes an identity, when you substitute a= -59, b= 36 there.\r\n" );
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document.write( "This check confirms that the found values are correct solutions.\r\n" );
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