Solve the system of equations: y + 3x = 0, x - y = 4, x + y = -2

Question

Вопрос:

Solve the system of equations: y + 3x = 0, x - y = 4, x + y = -2

Ответ:

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Accepted Answer

System of Equations:

Equation 1: $$y + 3x = 0$$
Equation 2: $$x - y = 4$$
Equation 3: $$x + y = -2$$

Hint: We can solve this system by substitution or elimination. Let's use substitution. From Equation 1, we can express y in terms of x: $$y = -3x$$. Substitute this into Equation 2 and Equation 3.

Step-by-step solution:

Step 1: Express y from Equation 1.
$$y = -3x$$
Step 2: Substitute y in Equation 2.
$$x - (-3x) = 4$$
$$x + 3x = 4$$
$$4x = 4$$
$$x = 1$$
Step 3: Substitute x = 1 into the expression for y.
$$y = -3(1)$$
$$y = -3$$
Step 4: Check if the solution (x=1, y=-3) satisfies Equation 3.
$$x + y = -2$$
$$1 + (-3) = -2$$
$$-2 = -2$$

Answer: The solution to the system is x = 1, y = -3.