document.write( "Question 1130668: hi! what do x and y equal in this system of linear equation: 2x+3y=78 and 6x+5y=180 \n" ); document.write( "

Algebra.Com's Answer #747297 by ikleyn(52800) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " Instead of that nonsensical response from the tutor @MathLover1, i will try to produce something more adequate.\r
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document.write( "2x + 3y =  78      (1)\r\n" );
document.write( "6x + 5y = 180      (2)\r\n" );
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document.write( "Apply the elimination method.  Multiply eq(1) by 3 (both sides).  Keep the equation (2) as is.\r\n" );
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document.write( "6x + 9y = 234      (1')\r\n" );
document.write( "6x + 5y = 180      (2')\r\n" );
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document.write( "Now subtract eq(2') from eq(1'). the terms \" 6x \" will cancel each other, and you will get a single equation for only one unknown \"y\".\r\n" );
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document.write( "    (It is how the Elimination method works)\r\n" );
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document.write( "    9y - 5y = 234 - 180\r\n" );
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document.write( "       4y   =   54\r\n" );
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document.write( "        y   =   54/4  = 13.5.\r\n" );
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document.write( "Then from eq(1)   2x = 78 - 3*13.5 = 37.5  ====>  x = 37.5/2 = 18.75.\r\n" );
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document.write( "Answer.  x=  = 18.75;  y =  = 13.5.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I am very surprised on how the tutor @LoverMath1 treats these problems on solving equation systems.\r
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\n" ); document.write( "\n" ); document.write( "By applying this \"pluggable solver\", she turns / transforms / converts very serious educational task of teaching students
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