Question 134807
Let's solve by substitution
Given : {{{5m + n = 8}}}  and {{{3m -4n = 14}}}
{{{5m + n = 8}}}
{{{ n = 8 - 5m}}}

Now use that value of n and sub back into the second equation
{{{3m -4n = 14}}}
{{{3m - 4(8 - 5m) = 14}}}
{{{3m -32 + 20m = 14}}}
{{{23m = 46 }}}
{{{ m = 2}}}

Use this value of m any equation to find n
{{{n = 8 - 5(2)}}}
{{{n = -2}}}

verify the answer
Does {{{3*(2) -4*(-2) = 14}}} ???
{{{ 6 + 8 = 14 }}} check!