To solve the system of linear equations 3 x + 5 y = 2 and 6 x + 10 y = 8 by using the linear combination method, Laura correctly multiplied the first equation by –2 to get Negative 6 x minus 10 y = negative 4 and then correctly added the equations Negative 6 x minus 10 y = negative 4 and 6 x + 10 y = 8 to get 0 = 4. How many solutions are there to the system of equations?

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

18.75 gallons

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