MHB Substitution Method to solve linear simultaneous equation

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The discussion focuses on solving a system of linear equations using the substitution method. The user transformed the equations into a common denominator and derived two equations: 5y - 5x = 1 and 5y + 2x = 5. After substituting, they found x = 4/7, but expected the solution to be x = 0. A suggestion was made to multiply the first equation by 6 and simplify to potentially correct the solution. The conversation highlights the importance of careful manipulation of equations in the substitution method.
Yazan975
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What I have done:

I changed all fractions to common denom and that gave me

5y-5x=1 (1) *I numbered the fractions
5y+2x=5 (2)

Then: 5y=5-2x

Substitute into equation 1
(5-2x)-5x=1
5-7x=1
x=4/7

Thing is my answer says I should be getting x=0

Any hints?
 

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When you multiply the first equation by $6$ and simplify, you should get $y-5x=1$.
 

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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