Question

Determine which equations are linear equations in the variables x, y, and z. If any equation is not linear, explain w hy not.
\(\displaystyle{x}-\pi{y}+\sqrt[3]{5}={0}\)

Answer 1

Step 1
Consider the given equation \(\displaystyle{x}-\pi{y}+\sqrt[3]{5}={0}\).
Step 2
Coefficient of x is 1, that of y is -π, and that of z is \(\sqrt[3]{5}\).
Since all these coefficients are constant \((\displaystyle{1},\pi,\sqrt[3]{5})\), and the constant term, (that is, 0) is also constant.
Thus, it can be concluded that the given equation \(\displaystyle{x}-\pi{y}+\sqrt[3]{5}={0}\) is linear.