MHB How to Solve a System of Three Equations with Three Unknowns?

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To solve the system of equations a + b = 3, -b + c = 3, and a + 2c = 10, one approach is to first combine the first two equations to form a new equation: a + c = 6. Next, subtract this new equation from the third equation, a + 2c = 10, to isolate c. Once the value of c is determined, substitute it back into the first equation to find a, and then use either the first or second original equation to calculate b. This method effectively simplifies the problem into a manageable two-variable system. The solution process demonstrates the systematic approach to solving multiple equations with unknowns.
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How do I do:

a + b = 3
-b + c = 3
a + 2c = 10
 
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I would begin by adding the first two equations, and then you have the 2X2 system:

$$a+c=6$$

$$a+2c=10$$

Now, try subtracting the first from the second to get $c$, then use the first along with the value for $c$ to find $a$, and then once you have $a$ and $c$, you can use either the first or second equation from the original system to find $b$. :D

What do you find?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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