I feel stupid asking this but I'm stuck I have three unknowns (x,y and z) and two equations (300-y=z and x-100=z) and while I know how to find thee unknowns with three equations, I'm just hitting a wall here - My immediate thought was to get a third equation from the other two just the logic seems to be circular and I'm going nowhere - can someone help please?
2026-04-29 19:55:47.1777492547
Simultaneous equations - Two equations, Three unknowns
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There are an infinite number of solutions. See the rank-nullity theorem. As others mentioned, the solution space forms "an affine subspace of dimension 1", also called a line ;)
This means you have some freedom. So just set $z=c$.
Then the solution is: $$ x = c + 100 $$ $$ y = 300 - c $$ which will be true for any $c\in\mathbb{R}$ that you pick. (Going over all the values of $c$ will then form a line in 3D).