Given that two lines are
y = 3.5x + 15
and y = 4x + 10
The condition for two lines to intersect is

So, for the given lines the condition will be

Since it had satisfied the condition then the given lines will intersect.
Now to find the intersecting point we will put both the equation equal.
3.5x + 15 = 4x + 10
4x - 3.5x = 15 - 10
0.5x = 5
x = 5/0.5 = 50/5
x = 10
So from the equation (i)
y = 3.5x + 15
y = 3.5 (10) + 15 = 35 + 15 = 50
y = 50
Hence the intersecting point is (x,y) = (10,50)