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Quickest way of solving these type of questions?

8 Answers

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Replace the symbols with letters for your own sanity, gather like symbols, and add, multiple and subtract and substitute the other three equations into each other like normal.

So:
r = 4t  ....1)

s  + 2t = c   .....2)

3s = c + t  .....3)

-x = 2c-2r .....4)

2) + 2 * 3) =>  
7s + 2t = 3c + 2 t,    <=>  7s = 3c
into 2) gives

t = (2c/7) .... 5)

so 5) and 1) into 4) -x = 7t - 8t = -t
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I used substitution.  My answer is:  ? = one triangle
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You can think of it as a code where a symbol represents a number, probably a digit.

You can replace symbols with their equivalent expressions to simplify things, e.g. the first two lines give you expressions for the long rectangle and the circle, which you can swap into the last lines
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replace all the shapes with variables,
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I never thought of replacing symbols with numbers. A lot of people aren't taught these types of problems in school.
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4 equations and 4 unknowns ..so I'd suggest using the matrix determinant method for(after denoting each symbol with a letter so it's easier). It's pretty quick and easy. Used to do a lot of these in highschool
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This is just a simple linear system of 4 equations in 4 unknowns. You could keep substituting until you have an answer for each variable, or if you wish, you can arrange the terms into an augmented matrix and reduce it to RREF.

 I'd opt for substitution here, given the simplicity of the system. It's usually not worth the hassle to matrix algebra on these types of "viral math problems stumping the internet!"
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Subtract the rectangle

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