Question

how to find the point of intersection of x + 2y = 5 and x - 3y = 7

Answer 1

1)substitution method.
x+2y=5                          ,                  x-3y=7
x=5-2y  .........(1)           ,                  x=7+3y .............(2)\
substitute eq .....(1) in eq.....(2)
5-2y=7+3y
-3y-2y=7-5
-5y=2
y=-2/5

substitute y value in eq ......(1)
x=29/5

(x,y)=(29/5,-2/5)

Answer 2

You can find the point of intersection by solving these two eqn.
                             x+2y=5
                             x-3y=7
                           -   +     -
                         _________
                            5y=-2
                        ⇒y=-2/5
So x=5-2y
    x=  5+4/5
⇒x=29/5

So the point of intersextion is (x,y)=(29/5,-2/5)