Question 1082404
Using solving by elimination, what are the possible numbers you could multiply the following system by to eliminate a variable? 
{2x-3y=5 }
{-3x+7y=12}
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One way is to multiply the first equation by 3 and the 2nd equation by 2:

{{{ 6x - 9y = 15 }}}
{{{ -6x +14y = 24 }}}

Adding them together eliminates x:

{{{  0x + 5y = 39 }}}  —>  {{{ 2x = 5 + 3y = 25/5+3(39/5) = 142/5 }}}  ==>  {{{ x = 71/5 }}}

{{{ x=71/5 }}} and {{{ y=39/5 }}}

—
Check: {{{ 2x - 3y = 2*(71/5) - 3(39/5) = 142/5 - 117/5 = 25/5 = 5 }}} (ok)