Question

Eliminating a Variable

Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system.

$\left\{\begin{array}{l}3x+y+z=4\\ -x+y+2z=0\\ x-2y-z=-1\end{array}\right.$

Eliminate the x-term from the second equation.

Short answer

Hence after eliminating x from the second equation, the new equivalent system is: $\left\{\begin{array}{l}3x+y+z=4\\ -y+z=-1\\ x-2y-z=-1\end{array}\right.$

Step-by-step solution

Step 1. Given information

We are given the set of linear equations that is-

$\left\{\begin{array}{l}3x+y+z=4\\ -x+y+2z=0\\ x-2y-z=-1\end{array}\right.$

Step 2. Concept used

We have to eliminate x term from the second equation and then we have to write the new equivalent system.

Step 3. Calculation

We have to eliminate x from the second equation which can be done by adding it with the third equation.

So let us add the second equation with the third equation, we get

$-y+z=-1$

Now we are replacing the second equation with the above equation, we get the following equilateral triangular system:

$\begin{array}{l}3x+y+z=4\\ -y+z=-1\\ x-2y-z=-1\end{array}$