[problem 9]

Solve the following systems of equations

4x^2 - 2y^2 = 4

x^2 + y^2 = 10

Guest Apr 19, 2019

#1**+2 **

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. :)

Melody Apr 19, 2019

#2**+2 **

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 !

ElectricPavlov Apr 19, 2019

#3**+1 **

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 )

CPhill Apr 19, 2019