I’m solving a three-variable system in which one of the given equations has a missing term, so it will not be necessary to use any of the original equ

The given statement is "I’m solving a three-variable system in which one of the given equations has a missing term, so it will not be necessary to use any of the original equations twice when I reduce the system to two equations in two variables".
Consider the three-variable system in which one of the given equation has a missing term as follows.
$a_{1}x+b_{1}y+c_{1}z=d_1$
$a_{2}x+b_{2}y+c_{2}z=d_2$
$a_{3}x+b_{3}y=d_3$
Reduce the system of equations to simple equations with 2 variable, it is easy to perform in one step, given the missing term in an equation.
Eliminate the variable z in first two equations, to obtain the equation in two variables x and y, it is perform with the third equations in the original system.
Perform the elimination of one variable in two steps also possible, so in this case can solve only one step.
This implies that it will not be necessary to use any of the original equations twice when I reduce the system to two equations in two variables
Therefore, the given statement make sense.