Solve the system of equations: x + y = 1, y - x = 3, 2x + y = 0

Question

Вопрос:

Solve the system of equations: x + y = 1, y - x = 3, 2x + y = 0

Ответ:

ФИО:Телефон:Емаил:Полное описание сути нарушения прав (почему распространение данной информации запрещено Правообладателем):

Accepted Answer

System of Equations:

Equation 1: $$x + y = 1$$
Equation 2: $$y - x = 3$$
Equation 3: $$2x + y = 0$$

Hint: This is an overdetermined system (3 equations, 2 variables). We will solve the first two equations and then check if the solution satisfies the third equation. Let's use elimination.

Step-by-step solution:

Step 1: Solve the first two equations using elimination.
Add Equation 1 and Equation 2:
$$(x + y) + (y - x) = 1 + 3$$
$$2y = 4$$
$$y = 2$$
Step 2: Substitute y = 2 into Equation 1.
$$x + 2 = 1$$
$$x = 1 - 2$$
$$x = -1$$
Step 3: Check if the solution (x=-1, y=2) satisfies Equation 3.
$$2x + y = 0$$
$$2(-1) + 2 = 0$$
$$-2 + 2 = 0$$
$$0 = 0$$

Answer: The solution to the system is x = -1, y = 2.