Given the two balance scales, we might ask how much the green triangle weighs.

Or perhaps, we might want to know the value of $t$ in the equations $\begin{aligned} s + t &= 3 \\ 2s + t &= 5. \end{aligned}$ In either case, we can use the same approach: the elimination method.

Elimination depends on this fact:

We can always keep a scale in balance by removing (or adding) equivalent quantities on both sides.

What's happening here? We know from the first balance that a square and a triangle are *equivalent* to $3$ (they are in balance and must therefore weigh the same). Therefore, on the second balance, we can remove a square and a triangle from the *left* and $3$ from the *right*, and the scale will still be in balance.

Note that although what we removed on the right *looks* different from what we removed on the left, we know that they are the *equivalent* because the first scale showed us.

From here, we can solve directly: the blue square equals $2,$ so the green triangle must equal $1.$

Let's look at the same approach but this time with an algebraic representation: $\begin{aligned} s + t &= 3 \\ 2s + t &= 5. \end{aligned}$ Subtracting the first equation from the second, we get $\begin{aligned} 2s + t &= 5 \\ - (s + t) &= -(3) \\ \Rightarrow s &= 2. \end{aligned}$ Because $s=2$, we can conclude that $t=1$. By combining these equations, we found the solution very quickly.

Although the problem below looks cumbersome, if you approach it as an elimination problem — where combining the equations together lets you simplify — there's a straightforward path to the solution.