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Either `x+y or 9x+y=12`Either `x+y=5 or 4x+9y=30`Either `x+y=4 or x+9y=12`Either `x+y=5 or 9x+4y=30`

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DSolution :

Intercept form of line is `x/a+y/b=1`. <br> We know, the point which divides a line joining two points `(x_(1), y_(1))` and `(x_(2), y_(2))` in the ratio `m : n` is <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NDA_14Y_MATH_C07_E01_136_S01.png" width="80%"> <br> `((mx_(2)+nx_(1))/(m+n), (my_(2)+ny_(1))/(m+n))` <br> Case 1 : `m : n =2 : 3` <br> `:. (2, 3)=(((2)(a)+3(0))/(2+3), (2(0)+3(b))/(2+3))` <br> `implies (2, 3)=((2a)/5, (3b)/5)` <br> `implies (2a)/5=2 , (3b)/5=3` <br> `implies a=5, b=5`. <br> `:.` Equation of line is `x/5+y/5=1 implies x+y=5` <br> Case 2 : `m : n =3 : 2` <br> `:. (2, 3)=((3(a)+2(0))/(3+2), (3(0)+2(b))/(3+2))` <br> `implies (2, 3) =((3a)/5, (2b)/5)` <br> `implies (3a)/5=2, (2b)/5=3` <br> `implies a=10/3, b=15/2` <br> `:.` Equation of line is `x/(10/3)+y/(15/2)=1` <br> `implies (3x)/10+(2y)/15=1` <br> `implies 9x+4y=30`