Solve system of equations with product

Question

Is there a way to solve this system of equations?

$16s-9t=ts$

$107s-100t=ts$

for t and s? Thanks in advance.

Answer 1

Hint: $16s-9t=107s-100t$, $91s=91t$, $s=t$. Now if we substitute $s$ in the first equation, we'll get $16t-9t=t^2$ which is quite easy to solve.

Answer 2

Hint: the right-hand sides are the same, so you also need: $$16s-9t=107s-100t \iff s = t$$ Plug this back into one of the initial equations to find two solutions.