Representing the following line using the symmetric form and parametric equations {█(x+y+z+1=0@2x-y+4z+4=0)┤ .

To represent the given line using symmetric form, we can eliminate one variable from the two equations and write the equation in terms of the remaining two variables.

From the first equation, we have:

x + y + z + 1 = 0

=> x = -y - z - 1

Substituting this value of x in the second equation, we get:

2(-y - z - 1) - y + 4z + 4 = 0

=> -3y + 6z = -6

=> y - 2z = 2

Now, we can write the equation of the line in symmetric form as:

x/(-1) = y/(-2) = z/1

or

x = -y/2 = z

To represent the line using parametric equations, we can assume a value for one of the variables, say z, and then solve for the other two variables. Let's assume z = t, where t is some parameter. Then, we have:

x = -y/2 = t

Solving for y, we get:

y = -2t

Therefore, the parametric equations of the line are:

x = t

y = -2t

z = t

where t is any real number.