Question

X² + y² = 17,x - y = 3​

Answer 1

Ответ:

(-1;-4)  и (1;4)

Объяснение:

x² + y² = ($\sqrt{17}$)² уравнение окружности с центром в 0 и радиусом √17

x - y = 3 ⇒ y = x-3

дальше строить и графически смотреть - картинка или аналитически систему решать вот так:

y = x-3

x² + (x-3)²-17 = 0

2x²-6x -8 =0

x²-3x-4 = 0

D = 9+16 = 25

x₁ ₂ = (3±5)/2

x₁ = -1, y₁ = -4

x₂ = 4, y₂ = 1

тот же рез-т

Answer 2

To solve the system of equations $x^2 + y^2 = 17$ and $x - y = 3$, you can use the method of substitution or elimination. I'll use the elimination method here.

First, let's rewrite the second equation ($x - y = 3$) in terms of one variable. You can solve it for $x$:

$x = 3 + y$

Now, substitute this expression for $x$ into the first equation ($x^2 + y^2 = 17$):

$(3 + y)^2 + y^2 = 17$

Now, expand and simplify the equation:

$9 + 6y + y^2 + y^2 = 17$

Combine like terms:

$2y^2 + 6y + 9 = 17$

Subtract 17 from both sides to isolate the quadratic terms:

$2y^2 + 6y - 8 = 0$

Divide the entire equation by 2 to simplify:

$y^2 + 3y - 4 = 0$

Now, you can solve this quadratic equation for $y$. You can factor it:

$(y + 4)(y - 1) = 0$

Set each factor equal to zero and solve for $y$:

1. $y + 4 = 0$ ⟹ $y = -4$
2. $y - 1 = 0$ ⟹ $y = 1$

So, there are two possible values for $y$: $y = -4$ and $y = 1$.

Now that you have the values of $y$, you can find the corresponding values of $x$ using the equation $x = 3 + y$:

1. When $y = -4$, $x = 3 + (-4) = -1$.
2. When $y = 1$, $x = 3 + 1 = 4$.

Therefore, the solution to the system of equations is:

$x = -1$ and $y = -4$

OR

$x = 4$ and $y = 1$