Question

These exercises refer to the following system:

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

If we add $2$ times the first equation to the second equation, the second equation becomes_______$=$________

Short answer

$x+3z$and $1$

Step-by-step solution

Step 1. Given information

We are given equation that is-

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

Step 2. Concept used

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

Step 3. Calculation

Consider the equations:

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

The objective is to add two times the first equation to the second equation. Multiply the equation $\left(1\right)$by 2

$\begin{array}{l}2(x-y+z)=2\times 2\\ 2x-2y+2z=4\end{array}$

Add two times the first equation to the second equation to obtain that,

Therefore, we add 2 times the first equation to the second equation, the second equation becomes $x+3z=1$.