document.write( "Question 1130782: Solve the systems of equations by using the substitution method. (If the system is dependent, enter a general solution in terms of c.
\n" ); document.write( "{18x− 12y=24
\n" ); document.write( " −6x+ 4y= 12
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Algebra.Com's Answer #747395 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "18x - 12y = 24     (1)\r\n" );
document.write( "-6x +  4y = 12     (2)\r\n" );
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document.write( "To reduce coefficients (and make your solution easier), divide eq(1) by 6 (both sides); divide eq(2) by -2 (both sides). \r\n" );
document.write( "You will get\r\n" );
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document.write( "3x - 2y =   4      (3)\r\n" );
document.write( "3x - 2y = -12      (4)\r\n" );
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document.write( "From this point, you can just see that the system is inconsistent:  left sides of equations (3) and (4) are identical,\r\n" );
document.write( "while their right sides are different.  So, the system has no solution/solutions.\r\n" );
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document.write( "But I will follow instructions and will apply the substitution method.\r\n" );
document.write( "Let's see what will happen.\r\n" );
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document.write( "From equation (3), I express 3x = 4 + 2y  and substitute it into equation (4). I get\r\n" );
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document.write( "(4 + 2y) - 2y = -12\r\n" );
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document.write( "2y - 2y = -12 - 4\r\n" );
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document.write( "0 = -16.                   (*)\r\n" );
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document.write( "Thus we got self-contradictory equation (*), which means that the original system has no solution/solutions.\r\n" );
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document.write( "It confirms our conclusion, which was made earlier.\r\n" );
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