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# Substitution equations

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1. Can anyone solve this substitution equation?
2. (Original post by w.mitchell)

Can anyone solve this substitution equation?
Is this something you need help with? Or just a fun little puzzle
3. A bit of both really! It's been bugging me all evening and I was wondering if someone else wanted to try and work it out
4. (Original post by w.mitchell)
A bit of both really! It's been bugging me all evening and I was wondering if someone else wanted to try and work it out
To get you started, try considering the second column sum and the third row sum as simultaneous equations.
5. (Original post by w.mitchell)
A bit of both really! It's been bugging me all evening and I was wondering if someone else wanted to try and work it out
You first need to form equations for each row/column
From there you can substitute in values to work out the value of one of the shapes, then use that in another equation to find another value ect until you find all three

This is what I got plus my working, just ask if you don't understand anything
Spoiler:
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6. I got square=5
triangle=17
circle=8
7. (Original post by KaylaB)
x
I concur though this can be done a little more succinctly.
Spoiler:
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, from which we deduce .
Subbing this in to we get .

ETA: It's also worth noting that as this system is over-determined, one should check that the equations are consistent, though I guess we're assuming a solution exists.
8. (Original post by joostan)
I concur though this can be done a little more succinctly.
Spoiler:
Show
, from which we deduce .
Subbing this in to we get .
I know, I was trying to write it out properly so it'd be easy to follow, but I suppose I was perhaps a bit long-winded at points
9. (Original post by KaylaB)
I know, I was trying to write it out properly so it'd be easy to follow, but I suppose I was perhaps a bit long-winded at points
I'm not trying to pick holes at all, its just that with too much written down it can sometimes be more confusing.
I also edited in a comment regarding ensuring consistency, but that's not all that important to this discussion.
10. (Original post by joostan)
I'm not trying to pick holes at all, its just that with too much written down it can sometimes be more confusing.
I also edited in a comment regarding ensuring consistency, but that's not all that important to this discussion.
It's fine I understand, it just helps me in the long run
11. Thanks so much to everyone that helped with this - makes complete sense now!

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