Question 29715
{{{ 15x + 11y = 132 }}}
{{{  2x +  3y =  59 }}}
to solve, we can solve for x in the 2nd equation and plug it into the first to find y.
{{{  2x +  3y =  59 }}} subtract 3y from both sides
{{{  2x = 59 -3y }}} divide all parts by 2
{{{  2x/2 = 59/2 -3y/2 }}}
{{{  x = 59/2 -3y/2 }}} plug this back into equation #1
{{{ 15x + 11y = 132 }}}
{{{ 15(59/2 -3y/2) + 11y = 132 }}} distribute 15 to the quantity
{{{ 885/2 -45y/2) + 11y = 132 }}} change the fractions to a common denom of 2
{{{ 885/2 -45y/2 + 11y(2)/(2) = 132(2)/(2) }}} drop the denoms
{{{ 885 -45y + 11y(2) = 132(2) }}} multiply
{{{ 885 -45y + 22y = 264 }}} combine like terms
{{{ 885 - 23y = 264 }}} subtract 885 from both sides
{{{ -23y = 264 - 885 }}}
{{{ -23y = -621 }}} divide by -23
{{{ y = 27 }}}
pick either of the equations and plug y=27 in.
{{{  2x +  3y =  59 }}}
{{{  2x +  3(27) =  59 }}} multiply
{{{  2x +  81 =  59 }}} subtract 81 from both sides
{{{  2x  =  -22 }}} divide both sides by 2
{{{x = -11 }}}
the solution, or ordered pair, where the two lines cross is :
(-11,27)