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Given
\n" ); document.write( "(1) x/2 - y/3 = 5/6 and
\n" ); document.write( "(2) x/5 - y/4 = 57/10
\n" ); document.write( "Clear the fractions in (1) by multiplying both sides of the equation by 6 and get
\n" ); document.write( "(3) 3x - 2y = 5
\n" ); document.write( "Clear the fractions in (2) by multiplying both sides of the equation by 20 and get
\n" ); document.write( "(4) 4x - 5y = 114
\n" ); document.write( "Now solve (3) for x and get
\n" ); document.write( "(5) 3x = 2y + 5 or
\n" ); document.write( "(6) x = (2/3)y + 5/3
\n" ); document.write( "Now substitute x of (6) into (4) and get
\n" ); document.write( "(7) 4*((2/3)y + 5/3) - 5y = 114 or
\n" ); document.write( "(8) (8/3)y + 20/3 - 5y = 114 or
\n" ); document.write( "(9) (8/3 - 5)y = 114 - 20/3 or
\n" ); document.write( "(10) ((8-15)/3)y = (342-20)/3 or
\n" ); document.write( "(11) -(7/3)y = 322/3 or
\n" ); document.write( "(12) -7y = 322 or
\n" ); document.write( "(13) y = -322/7 or
\n" ); document.write( "(13) y = -46
\n" ); document.write( "Use y of (13) in (6) to get x
\n" ); document.write( "(14) x = (2/3)(-46) + 5/3 or
\n" ); document.write( "(15) x = (-92 + 5)/3 or
\n" ); document.write( "(16) x = -87/3 or
\n" ); document.write( "(17) x = -29
\n" ); document.write( "Check this pair with (2).
\n" ); document.write( "Is (-29/5 -(-46)/4 = 57/10)?
\n" ); document.write( "Is ((-29*4 + 46*5)/20 = 57/10)?
\n" ); document.write( "Is ((-116 + 230)/20 = 57/10)?
\n" ); document.write( "Is (114/20 = 57/10)?
\n" ); document.write( "Is (57/10 = 57/10)? Yes
\n" ); document.write( "Answer: The solution pair, using fraction clearing and substitution, is
\n" ); document.write( " (-29,-46) \n" ); document.write( "