Why isolate n in the x-component for finding speed on a banked turn?

[aron silvester]

Homework Statement

The question wants us to find the velocity that the car can take without assistance from friction. The friction, in this case, is the normal friction, weight friction, and the static friction (pointing towards the right). I understand how it got ncos(15) - w = 0 for the y component. What I don’t understand is why do we need to isolate n, which equaled to mg/cos(15), and plug that inside the n for the x-component?

[/B]

Homework Equations

It's all in part 1

The Attempt at a Solution

It's all in part 1

 

[kuruman]

Because you have a system of two equations and two unknowns, n and v. You eliminate n in order to solve for v.