i need help please

Rearrange both equations so that   y^2 is the subjects of the equation.

Then put them together to solve for x

Give that a go and post your working.  Then, if you need it, we can help you more.  :)

Another option:   re arrange the second equation to this: y^2 = 10 - x^2      Now substitute THIS value of y^2 into the FIRST equation and solve for 'x'.....once you have an 'x' value(s)....sub this value of x into one of the original equations to calculate the corresponding 'y' value(s).....

    let us know what  you find!

A third option would be to graph the two equations and look for the points that they intersect......   try that too !  

4x^2 - 2y^2 = 4  ⇒  2x^2 -y^2 = 2   (1)

x^2 + y^2  = 10   (2)

Add (1) and (2)   to get

3x^2 =  12         divide both sides by 3

x^2  = 4           take both roots

x = ±√4

So

x = 2        and     x  = -2

And when x is either of these values, we can find y  as

(2)^2 + y^2  = 10

4 + y^2  = 10

y^2  =  6

y  = ±√6

So.....we have these 4 solutions

(2, √6)  (2, -√6)  ( -2, √6)   (-2, - √6 )

FYI:    Here is the graph