Solve the system of equations 1/4x+4/5y=2 and 5/16x-1/5y=3

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You need to solve for x and y the given system of equations, hence, you may use substitution method, thus, you may use the top equation to write x in terms of `y` , such that:

`(1/4)x = 2 - (4/5)y => x = 4(2 - (4/5)y) => x = 8 - (16/5)y`

Replace `8 - (16/5)y` for `x` in the bottom equation, such that:

`(5/16)(8 - (16/5)y) - (1/5)y = 3`

`40/16 - (5/16)*(16/5)y - (1/5)y = 3`

`10/4 - y - (1/5)y = 3`

Isolate the terms that contain y to the left side, such that:

`-y - y/5 = 3 - 10/4 => -y - y/5 = 3 - 5/2`

You need to bring the terms to the left side to a common denominator, such that:

`(-5y - y)/5 = 3 - 5/2`

`-6y/5 = (6 - 5)/2 => -6y/5 = 1/2 => -6y = 5/2 => y = -5/12`

Replace -`5/12` for `y` in equation `x = 8 - (16/5)y` , such that:

`x = 8 - (16/5)(-5/12) => x = 8 + 16/12 => x = 8 + 4/3 => x = (24 + 4)/3 => x = 28/3`

Hence, evaluating the solution to the given system, using substitution, method, yields `x = 28/3, y = -5/12.`

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