Please help with systems of equations need super urgent
*Check the pic*

y = ±5

x = ±6

Step-by-step explanation:

Here we have the system:

x^2 + y^2 = 61

x^2 - y^2 = 11

Notice that we have both variables squared, then we can define:

x^2 = X

y^2 = Y

And write our system as:

X + Y = 61

X - Y  = 11

To solve this, the first step is to isolate one of the variables in one of the equations, i will isolate X in the second equation:

X = 11 + Y

Now we can replace this in the other equation to get:

(11 + Y) + Y  = 61

Now we can solve this for Y

11 + 2*Y = 61

2*Y = 61 - 11 = 50

Y = 50/2 = 25

Y = 25

And remember that Y = y^2

then:

y^2 = 25

y = √25 = ±5

And using the equation: X = 11 + Y

X = 11 + 25 = 36

X = x^2 = √36 = ±6

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: