Question

Is the System of Equations Linear?

State whether the equation or system of equations is linear.

$x^2+y^2+z^2=4$

Short answer

Hence the equation $x^2+y^2+z^2=4$ is not linear equation.

Step-by-step solution

Step 1. Given information

We are given equation that is-

$x^2+y^2+z^2=4$

Step 2. Concept used

An equation that is written for two different variables is known as a linear equation.

Step 3. Calculation

We have to state whether the given expression is a linear equation or not.

Since an equation is a linear equation when it is in the form $ax+by+cz+d=0$

where $a,b,c,d$ are constant.

And in our case, the given equation has exponents of 2

Thus the given equation is non-linear.

So, $x^2+y^2+z^2=4$is a non-linear equation.