solve the system by addition method

7x^2+y^2=49
7x^2-y^2=49

add the equations and get:

14x^2=98
x= sqrt (98/14)

thanks, but I don't believe that is correct.

To solve the system of equations by the addition method, we can add the two equations together. This will allow us to eliminate one of the variables and solve for the other.

Let's add the two equations:

(7x^2 + y^2) + (7x^2 - y^2) = 49 + 49

Combining like terms, we get:

14x^2 = 98

Now, let's divide both sides of the equation by 14 to solve for x^2:

(14x^2) / 14 = 98 / 14

x^2 = 7

Next, we need to substitute the value of x^2 (which is 7) back into one of the original equations to solve for y^2.

Let's choose the first equation:

7(7) + y^2 = 49

49 + y^2 = 49

Subtract 49 from both sides:

y^2 = 0

Now, we have values for both x^2 and y^2. Taking the square root of both sides, we can find the values of x and y:

x = √7 or -√7
y = 0 or 0

So, the solution to the system of equations is:
(x, y) = (√7, 0) or (-√7, 0)