Question

Is the System of Equations Linear?

State whether the equation or system of equations is linear.

$\left\{\begin{array}{l}x-2y+3z=10\\ 2x+5y=2\\ y+2z=4\end{array}\right.$

Short answer

Hence all the equations in the system of equations is linear:

$\begin{array}{l}x-2y+3z=10\\ 2x+5y=4\\ y+2z=2\end{array}$

Step-by-step solution

Step 1. Given information

We are given the set of linear equations that is-

$\left\{\begin{array}{l}x-2y+3z=10\\ 2x+5y=4\\ y+2z=2\end{array}\right.$

Step 2. Concept used

An equation that is presented by the combination of two variables and a constant is known as a linear equation.

Step 3. Calculation

The given system of equation is linear as all the equation in the system of equations has the form $ax+by+cz+d=0$ where $a,b,c,d$ are constants.

So, the given system of equations is linear.