Question

Give an example of a system of three equations in three variables that has$\left(-3,5,2\right)$as a solution. Show that the ordered triple satisfies all three equations.

Short answer

The three equations in three variables are

$\begin{array}{l}x+y+z=4\\ x+2y+3z=13\\ 2x+3y+z=11\end{array}$

Step-by-step solution

Step-1 –Satisfying the equations x+y+z

The given solution is$\left(-3,5,2\right)$

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

So,$x+y+z=4.$

Step-2 –Satisfying the equations x+2y+3z

The given solution is$\left(-3,5,2\right)$

$\begin{array}{l}x+2y+3z=-3+2\left(5\right)+3\left(2\right)\\ =-3+10+6\\ =7+6\\ =13\end{array}$

So, $x+2y+3z=13.$

Step-3 –Satisfying the equations 2x+3y+z

The given solution is$\left(-3,5,2\right)$

localid="1648724175920" $\begin{array}{l}2x+3y+z=2(-3)+3\left(5\right)+2\\ =-6+15+2\\ =9+2\\ =11.\end{array}$

So, $2x+3y+z=11.$