document.write( "Question 154804: Solve each of the following systems by the elimination method
\n" ); document.write( "1/4x - 1/6y = -2
\n" ); document.write( "-1/6x + 1/5y = 4
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #113987 by orca(409) $\"\"$ $\"About$

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$\"%281%2F4%29x-%281%2F6%29y=-2\"$ ..............(1)
\n" ); document.write( " $\"%28-1%2F6%29x%2B%281%2F5%29y=4\"$ ..............(2)
\n" ); document.write( "Multiplying equation (1) by 12,equation (2) by 30 to clear fractions, we have\r
\n" ); document.write( "\n" ); document.write( " $\"3x-2y=-24\"$ .....................(3)
\n" ); document.write( " $\"-5x%2B6y=120\"$ ....................(4)
\n" ); document.write( "Multiplying equation (3) by 3, the systems becomes:
\n" ); document.write( " $\"9x-6y=-72\"$ .....................(5)
\n" ); document.write( " $\"-5x%2B6y=120\"$ ....................(6)
\n" ); document.write( "Adding equations(5) and (6)together, we have
\n" ); document.write( " $\"9x-6y%2B%28-5x%2B6y%29=-72%2B120\"$
\n" ); document.write( "Simplifying, we have
\n" ); document.write( " $\"9x-6y-5x%2B6y=48\"$
\n" ); document.write( " $\"4x=48\"$
\n" ); document.write( " $\"x=12\"$
\n" ); document.write( "Substituting x = 12 into equation(3), we obtain:
\n" ); document.write( " $\"3%2A12-2y=-24\"$
\n" ); document.write( "Solving for y, we have
\n" ); document.write( " $\"36-2y=-24\"$
\n" ); document.write( " $\"36%2B24=2y\"$
\n" ); document.write( " $\"60=2y\"$
\n" ); document.write( " $\"30=y\"$
\n" ); document.write( "So
\n" ); document.write( " $\"y=30\"$
\n" ); document.write( "Thus the solution is:
\n" ); document.write( "x = 12
\n" ); document.write( "y = 30\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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