2x+5y=9         
‌x−‌3y=−1]×2         –––––––––––––––
Subtracting we get   
11y=11Substituting in second equation we get
x=–1+3⇒x=2Point of intersection is (2, 1)
We can write equation of line as
y–1=m(x–2)⇒y–1=mx–2m⇒mx–y+(1–2m)=0Writing for distance from origin,
⇒1+4m2−4m=5m2+5⇒m2+4m+4=0⇒(m+2)2=0⇒m=−2
Equation of line,
y−1=−2(x−2)⇒y−1=−2x+4⇒2x+y=5