Question

Is the System of Equations Linear?

State whether the equation or system of equations is linear.

$6x-\sqrt{3}y+\frac{1}{2}z=0$

Short answer

Hence the equation $6x-\sqrt{3}y+\frac{1}{2}z=0$ is a linear equation.

Step-by-step solution

Step 1. Given information

We are given equation that is-

$6x-\sqrt{3}y+\frac{1}{2}z=0$

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.

In our case $a,b,c,d$ is $6,-\sqrt{3},\frac{1}{2},0$ and $a,b,c$are not simultaneously zero.

Thus the equation is linear.

So, the given equation is a linear equation.