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

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SUMMARY

The discussion focuses on solving for the velocity of a car on a banked turn without frictional assistance. The key equations involve isolating the normal force (n) in the y-component equation, resulting in n = mg/cos(15°). This value of n is then substituted into the x-component equation to find the velocity (v). The necessity of isolating n arises from the requirement to eliminate one variable in a system of two equations to solve for the other.

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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?
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Homework Equations


It's all in part 1

The Attempt at a Solution


It's all in part 1
 
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Because you have a system of two equations and two unknowns, n and v. You eliminate n in order to solve for v.
 

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