Question

X²-y=0 X-2y=-1 Решить систему

Answer 1

Вот ответ.Спасибо за вопрос.

Answer 2

X²-y=0

X-2y=-1

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X²= y

X-2х²=-1

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X²= y

-х²= -1  ⇒ х²=1   ⇒х₁=1   х₂= -1  (при подстановке не подходит);

                              у=х²   у₁=1

Ответ: (1;1)

Answer 3

To solve the system of equations $x^2 - y = 0$ and $x - 2y = -1$, we can use either the substitution method or the elimination method. Let's use the elimination method in this case:

Step 1: Multiply the second equation by 2 to make the coefficients of $y$ in both equations the same:

$2(x - 2y) = 2(-1)$ $2x - 4y = -2$

Now, the system becomes:

$x^2 - y = 0$ ...(Equation 1) $2x - 4y = -2$ ...(Equation 2)

Step 2: Solve the second equation for $x$ or $y$ in terms of the other variable. Let's solve Equation 2 for $x$:

$2x = 4y - 2$ $x = 2y - 1$ ...(Equation 3)

Step 3: Substitute Equation 3 into Equation 1:

$(2y - 1)^2 - y = 0$

Step 4: Expand and simplify the equation:

$4y^2 - 4y + 1 - y = 0$

Step 5: Combine like terms and move all terms to one side of the equation:

$4y^2 - 5y + 1 = 0$

Step 6: Factor the quadratic equation:

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

Step 7: Set each factor to zero and solve for $y$:

$4y - 1 = 0$ or $y - 1 = 0$

$4y = 1$ or $y = 1$

$y = \frac{1}{4}$ or $y = 1$

Step 8: Now that we have the values of $y$, we can find the corresponding values of $x$ using Equation 3:

For $y = \frac{1}{4}$:

$x = 2y - 1 = 2\left(\frac{1}{4}\right) - 1 = \frac{1}{2} - 1 = -\frac{1}{2}$

For $y = 1$:

$x = 2y - 1 = 2(1) - 1 = 2 - 1 = 1$

So the solution to the system of equations is:

$x = -\frac{1}{2}$ and $y = \frac{1}{4}$

or

$x = 1$ and $y = 1$