Question 160022
Let's call the larger number L and the smaller one S.
1.{{{4L+3S=68}}}
2.{{{7L-5S=37}}}
Use eq. 1 to solve for L in terms of S.
1.{{{4L+3S=68}}}
{{{4L=68-3S}}}
{{{L=17-(3/4)S}}}
Now substitute this expression for L into eq. 2 and solve for S.
2.{{{7L-5S=37}}}
{{{7(17-(3/4)S)-5S=37}}}
{{{7(17-(3/4)S)-5S=37}}}
{{{119-(21/4)S-5S=37}}}
{{{-(21/4)S-(20/4)S=-82}}}
{{{-(41/4)S=-82}}}
{{{S=(82*4)/41}}}
{{{highlight(S =8)}}}
From eq. 1,
{{{L=17-(3/4)S}}}
{{{L=17-(3/4)8}}}
{{{L=17-6}}}
{{{highlight(L=11)}}}