Solve the system of equations algebraically x^2+2y^2=10 3x^2-y^2=9

We'll multiply the second equation by
2:

6x^2 - 2y^2 = 18 (3)

We'll
add the 3rd equation to the first one:

x^2 + 2y^2 + 6x^2 -
2y^2 = 10 + 18

We'll combine like
terms:

7x^2 = 28

x^2 =
4

x1 = 2 and x2 = -2

Now,
we'll substitute x = 2 in the 1st equation:

2^2 + 2y^2 =
10

4 + 2y^2 = 10

2y^2 =
6

y^2 = 3

y1 = sqrt3 and y2 =
-sqrt3

We'll substitute x = -2 in the 1st
equation:

4 + 2y^2 = 10

2y^2 =
6

y^2 = 3

y3 = sqrt3 and y4 =
-sqrt3

The solutions of the equation are the
ordered pairs: (2 ; sqrt3) ; (2 ; -sqrt3) ; (-2 ; sqrt3) ; (-2 ;
-sqrt3).