Question

Help x^2-y^2=24 4y+x=0

Answer 1

X=-4y
16y^2-y^2=24
y^2=24/15
y^2=8/5
y1=sqrt(8/5)
x1=-4sqrt(8/5)
y2=-sqrt(8/5)
x2=4sqrt(8/5)

Answer 2

To solve this system of equations, we can use the substitution method or the elimination method.

Let's use the substitution method:

From the second equation, we have x = -4y. Substituting this into the first equation, we get:

(-4y)^2 - y^2 = 24

16y^2 - y^2 = 24

15y^2 = 24

y^2 = 24/15

y = ±√(24/15) = ±√(8/5)

y = ±(2/√5)

Now, substituting y into the second equation to find x:

4y + x = 0

4(±2/√5) + x = 0

x = ∓(8/√5)

Therefore, the solutions to the system of equations are:

(x, y) = (-8/√5, 2/√5) or (8/√5, -2/√5).