Question

Решите методом алгебраического сложения систему уравнений

Answer 1

X-5y=3
5y-2x=4

Поменяем во втором уранвении местами переменные

x-5y=3
-2x+5y=4

Теперь можно легко сложить.

Получаем:

-x=7
x=-7

Подставим в любое уравнение наше -7 вместо X, чтобы узнать y.

5y-2*(-7)=4
5y+14=4
5y=-10
y=-10/5
y=-2

Answer 2

Solving the System of Equations using Algebraic Addition

To solve the system of equations using the method of algebraic addition, we need to find the values of x and y that satisfy both equations. Let's denote the equations as follows:

Equation 1: x^2 + y^2 = 20 Equation 2: 3x + y = 2

To solve the system, we can substitute the value of y from Equation 2 into Equation 1 and solve for x. Let's do that:

From Equation 2, we have y = 2 - 3x. Substituting this into Equation 1, we get:

x^2 + (2 - 3x)^2 = 20

Expanding and simplifying the equation, we have:

10x^2 - 12x - 16 = 0

Now, we can solve this quadratic equation to find the values of x. Using the quadratic formula, we get:

x1 = -0.8 x2 = 2

Next, we can substitute these values of x back into Equation 2 to find the corresponding values of y. Using Equation 2, we have:

y = 2 - 3x

Substituting x1 = -0.8, we get y1 = 4.4. Substituting x2 = 2, we get y2 = -4.

Therefore, the solutions to the system of equations are: - x1 = -0.8, y1 = 4.4 - x2 = 2, y2 = -4

Additional Equation

It seems that there is an additional equation mentioned: xy - 3y^2 = -24. Let's solve this equation as well.

We can rewrite the equation as follows:

xy + 2y^2 = 21

To solve this equation, we can use the values of x and y obtained from the previous step. Let's substitute these values into the equation:

For the first solution (x1 = -0.8, y1 = 4.4): xy - 3y^2 = (-0.8)(4.4) - 3(4.4)^2 = -24.32 - 68.64 = -92.96

For the second solution (x2 = 2, y2 = -4): xy - 3y^2 = (2)(-4) - 3(-4)^2 = -8 + 48 = 40

Therefore, the solutions to the additional equation are: - For x1 = -0.8, y1 = 4.4: xy - 3y^2 = -92.96 - For x2 = 2, y2 = -4: xy - 3y^2 = 40

Conclusion

In summary, the solutions to the system of equations and the additional equation are as follows:

System of Equations: - x1 = -0.8, y1 = 4.4 - x2 = 2, y2 = -4

Additional Equation: - For x1 = -0.8, y1 = 4.4: xy - 3y^2 = -92.96 - For x2 = 2, y2 = -4: xy - 3y^2 = 40

Please let me know if there's anything else I can help you with!