i need some help on my math homework?

Question

solve each equations for y to get two separate equations that could be entered on a graphing calculator.

x^2+y^2=4
4x^2+y^2=9
3x-2y^2=1
i need some help solving these questions step by step. I dont need the answers, i just need to know how to solve these

Answer 1

In each case solve for y², then take both square roots.
I'll do the first one. You do the others.
y² = 4-x²
So either
y = √(4-x²)
or
y = -√(4-x²).
If you enter both of these into your graphing calculator, you
will see the full curve. It's a circle.

Answer 2

a) (^ means exponent, "sqrt" means square root)
x^2 + y^2 = 4
y^2 = 4 - x^2
y = sqrt(4 - x^2)

b)
4x^2 + y^2 = 9
y^2 = 9 - 4x^2
y = sqrt(9 - 4x^2)

c)
3x - 2y^2 = 1
-2y^2 = 1 - 3x
2y^2 = 3x - 1
y^2 = (3x - 1)/2
y = sqrt[(3x - 1)/2]

All you have to do is remember that you can perform any operation on an equation as long as you remember that you have to perform the exact same operation on the entirety of both sides.
ie.
y^2 = 1 + x
You can square root the left side to give you "y" as long as you remember to square root ALL of the right side as a whole:
y = sqrt(1 + x), and not y = sqrt(1) + sqrt(x)

The same is true for addition or subtraction; subtract something from the left side and you have to do the same for the right side:
ie.
y + x = 1
Subtract "x" from both sides (I'll write out the steps more fully this time):
y + x - x = 1 - x
y + 0 = 1 - x
y = 1 - x

Note that I picked a value to subtract from both sides that would conveniently cancel the "x" on the left, to isolate "y".

Now, putting these together:
ie.
y^2 + x = 1
y^2 + x - x = 1 - x
y^2 + 0 = 1 - x
y = sqrt(1 - x)

Make sure you perform the operations in a logical order such that you end up with the desired form of the equation, as opposed to:
y^2 + x = 1
sqrt(y^2 + x) = sqrt(1)

... which is a little harder to deal with (as you would have to undo the sqrt operation before proceeding).

Answer 3

x^2+y^2=4
y^2=4-x^2
you cant take the sqrt
instead factor
y^2=(2+x)(2-x)

4x^2+y^2=9
y^2=9-4x^2
again factor
y^2=(3+2x)(3-2x)

3x-2y^2=1
2y^2=3x-1
divide by 2 so y coefficient is 1
y^2=3/2x-1/2