Ax + By + 20z = G, How would i get G? (Look at Description)

Question

x = 9

y = 8

z = -17

Ax+By+Cz=G

33x+17y+25z=8

32x-16y+8z=24

42x+6y+24z=18

38x-2y+18z=20

Ax+By+20z=G

my goal is to get G

another thing i found out is A + B = 2C

Answer 1

There are a whole lot of equations here, but I'm suspicious about the different format of the equations... it feels like it's trying to confuse us with lots of information.

We have 4 equations with x, y, z equal to a value... AND we're given x, y, z. This means we can spend a whole lot of time multiplying them out just to see if the equations are correct or not. But they won't help us with G, or the values A, B, or C.

So the x, y, z equations are irrelevant.

So that leaves us just your two G equations.

Ax + By + Cz = G

Ax + By + 20z = G

It doesn't matter what x, y, z are (although we are given these values), the only way both equations are true is if C = 20.

So you don't have two equations in G, you only have one, and it has three unknowns A and B and G. So there's no solution.

9A + 8y + 20(-17) = G

9A + 8B = G + 340

Even if we have an additional equation A + B = 2z it doesn't help us.

If you "found out" this equation from the above information, I can't see how you did it, sorry.

But even if we're also GIVEN this equation I doesn't change things much.

Because we know C=20 so A + B = 40

So now we can eliminate A (or B)... but that still leaves two unknows B and G (or A and G).