Linear Equations

[Deleted User]

Can someone explain to me why

x + 5y - squroot(2z) = 1

and

pi*x - squroot(2y)+ 1/3*z = 7^(1/3)

are considered to be linear equations?

[leflyi]

Glancing at the equations it seems to me that they are more of a 3 Dimensional plane rather than a linear expression..

Correct me if I am wrong though..

Edit : I messed up, meant to say 2 Dimensional linear expression :O meh

[abeybaby]

an equation is linear if its degree is 1. the degree of a polynomial is the highest power in a variable.
so x+5y^2 has degree 1 in x, and 2 in y.

I wouldnt call those linear equations, because the first is degree 1 in x, 1 in y, but 1/2 in z.
The second is degree 1 in x, 1 in z, but 1/2 in y. If all variables were degree 1 in all equations, then i would call them linear equations. since they are degree 1 only in x, i would say its a linear equation if x was a variable, but z and y were constants. If x,y and z were all variables, i wouldnt call this a set of linear equations. (also, being a plane doesnt mean youre not linear, x+y+z=1 and x+y+z=2 are linear equations).