Question 858042
First find the intersection of the two line.
{{{3x-4y=5}}}
{{{x-y=2}}}
Use eq. 2 to substitute for {{{x}}} in eq. 1,
{{{x=y+2}}}
.
.
{{{3(y+2)-4y=5}}}
{{{3y+6-4y=5}}}
{{{-y+6=5}}}
{{{-y=-1}}}
{{{y=1}}}
Then
{{{x=1+2}}}
{{{x=3}}}
Now find the equation of the line that goes through (0,0) and (3,2).
{{{m=(2-0)/(3-0)=2/3}}}
{{{y=mx+b}}}
{{{y=(2/3)x}}}
{{{3y=2x}}}
{{{-2x+3y=0}}}
{{{highlight(2x-3y=0)}}}