Answer:
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
