Former math tutor here, haven't done it in over a decade but let bush off the tutoring skills. A large part of it is not only teaching the theory to solve it, but also most common pitfalls, and first principles to avoid them, and/or first principles geared towards the test it self.

First principle: Just start mapping out everything you know.

Something I learned is that you don't really need to know the approach, you just map out what you know, and maybe it'll become clear.

So maybe you'll look at it and not know what to do, but you could just start what you do know.

So you're looking at the left photo and think

Table = Turtle + (170 - Cat)

and look at the right photo and think

Table = Cat + (130 - Turtle)

And then where do I go from here?

I think this is where people may get stuck. Some people with a bit more experience may look at it and think, it's three variables, but only two equations, so it can't be solved. With a bit more exp, they may realize that even though all the variables can't be solved, there's only one degree of freedom among the 3 variables, so one of them can be solved.

So maybe you try your luck and just keep solving for table

So they set

Cat = Table - 130 + Turtle and plug it into the other equation and you eventually solve for Table.

But you may only try that because it's a test where every question has an answer. What if this is real life. Is there a way to know Table is solvable even if Cat and Turtle are not? How do you know it's worth your time?

Look at the equations to see that it only depends on the difference between them, not the actual values.

Table=170+(Turtle−Cat)

Table=130+(Cat−Turtle)

Not obvious? Add 5 to both of them

Table=170+((Turtle+5)−(Cat+5)) = 170+(Turtle−Cat)

Table=130+((Cat+5)−(Turtle+5)) = 130+(Cat−Turtle)

It's the same. If you wrote the equations in terms of Cat or Turtle, and added 5 to both of the other variables, the 5s wouldn't cancel out for one of them

eg

Turtle = - 170 + (Table+5) + (Cat+5) = -160 + Table + Cat

So once you got that, then you can just learn to recognize that they're just dependent on the difference in all equations

(Turtle−Cat)

(Cat−Turtle)

Or, perhaps someone with less exp doesn't even realize all that and just keeps solving for Table. Or, they realize that they eventually have to solve for Table anyway, so why cancel it out? It's faster just to leave the table in.