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[problem 9] 
Solve the following systems of equations 
4x^2 - 2y^2 = 4
x^2 + y^2 = 10

 Apr 19, 2019
 #1
avatar+105654 
+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.  :)

 Apr 19, 2019
 #2
avatar+19832 
+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 !   cheeky

 Apr 19, 2019
 #3
avatar+104899 
+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 )

 

 

 

cool cool cool

 Apr 19, 2019
 #4
avatar+19832 
+2

FYI:    Here is the graph

 

 Apr 19, 2019
 #5
avatar+104899 
0

THX, EP!!!!

 

cool cool cool

CPhill  Apr 19, 2019

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