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The key here is to eliminate one of the variables; it doesn't matter whether we start by trying to get rid of x or y we will arrive at the same solution. For us to eliminate either x or y it is easiest to find a way of making the co-efficient (number before the x or y) the same in both equations by multiplying through by a number as follows.
If we take 5x+y=8 and multiply through by 2 (don't forget to multiply both sides), we get
So we now have 10x+2y=16 and 6x+2y=4
We can rearrange both equations to give 2y=10x-16=6x-4.
We have now eliminated y leaving us with 10x-16=6x-4
Rearranging gives 10x-6x=16-4 so 4x=12. Therefore x=3.
If we substitute this back into one of our original equations such as 5x+y=8, we get 15+y=8.
Therefore, x=3 and y=-7.see more
In order to solve this question, we need to use the chain rule when differentiating.
The chain rule formula is dy/dx= (dy/du)*(du/dx).
Differentiating with respect to x gives du/dx=3x2
We now have y=u0.5
Differentiating with respect to u gives dy/du=0.5u-0.5=0.5*(1+x3)-0.5
Therefore dy/dx= (dy/du)*(du/dx)= 0.5*(1+x3)-0.5*(3x2)= 1.5x2*(1+x3)-0.5see more