Question

[tex]\left \{ {{x^{2} + y^{2} =225} \atop {x^{2} - y^{2} =63}} \right.\\[tex]

Answer 1

Ответ:

(12;9), (-12;9), (12;-9), (-12;-9)

Объяснение:

$\left \{ {{x^{2} + y^{2} =225} \atop {x^{2} - y^{2} =63}} \right.$

Суммируем уравнения:

2x²=288

x²=144

x=±12

Если из первого уравнения вычесть второе, то получим

2y²=162

y²=81

y=±9

Answer 2

To find the solution to the system of equations:

1. $x^2 + y^2 = 225$
2. $x^2 - y^2 = 63$

You can solve this system of equations by using the method of substitution. First, we can rewrite the second equation in terms of either $x$ or $y$ and then substitute it into the first equation. Let's solve for $y^2$ in terms of $x$ using the second equation:

$x^2 - y^2 = 63$

Now, add $y^2$ to both sides of the equation to isolate $y^2$:

$y^2 = x^2 - 63$

Now, substitute this expression for $y^2$ into the first equation:

$x^2 + (x^2 - 63) = 225$

Combine like terms:

$2x^2 - 63 = 225$

Add 63 to both sides:

$2x^2 = 225 + 63$

$2x^2 = 288$

Now, divide by 2 to isolate $x^2$:

$x^2 = 144$

Now, take the square root of both sides to solve for $x$:

$x = \pm \sqrt{144}$

$x = \pm 12$

Now that we have found the values of $x$, we can use these values to find the corresponding values of $y$ using the equation $y^2 = x^2 - 63$:

For $x = 12$:

$y^2 = 12^2 - 63 = 144 - 63 = 81$

So, $y = \pm 9$

For $x = -12$:

$y^2 = (-12)^2 - 63 = 144 - 63 = 81$

So, $y = \pm 9$

So, the solution to the system of equations is:

1. $x = 12, y = 9$
2. $x = 12, y = -9$
3. $x = -12, y = 9$
4. $x = -12, y = -9$