Linear Equations

[Petenerd]

I'm just wondering if these are linear equations: Ax + By + C = 0, y = -2, xy = -12, x + y = -6, 3(x - 2y) + y = 7 - x, and x = y^2.

Can you tell me if one isn't a linear equation?

[Loren]

Yes. In fact two of them are not linear.

[Petenerd]

Really, I only found out that xy = -12 is not linear. Which is the other one?

[Mrspi]

Really, I only found out that xy = -12 is not linear. Which is the other one?

The degree of "xy" in xy = -2 is the sum of the exponents on the variables in that term: x^1 * y^1 gives a degree of (1 + 1), or 2. In a linear equation, no term has a degree higher than 1.

NOW...look at your other answer choices to see if any of them has a term of degree that is greater than 1.

[Subhotosh Khan]

Non-linear equation comes in if you have power less than 1 also. For example

y = 5 + x[sup:3nziv9g1]1/2[/sup:3nziv9g1]

is non-linear. In otherwords, if the power is anything except 1, the equation is non-linear (except the power of the constant term - for example:

y + 5[sup:3nziv9g1]1/2[/sup:3nziv9g1]x + 3[sup:3nziv9g1]1/3[/sup:3nziv9g1] = 0 is a linear equation.