How to find x and y in simultaneous equations? y^2-4xy+4y=1 3x^2-2xy=1
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We have to solve the simultaneous equation
y^2 - 4xy + 4y = 1 ...(1)
3x^2 - 2xy = 1 ...(2)
We see that it is not possible to isolate x in terms of y or y in terms of x using any of the equations.
In (1) we get y = 1/(y - 4x + 4)
In (2) we get x = 1/(3x - 2y)
As this is the case, we cannot the solve the system of simultaneous equations. Using a random solution of (1 , 1), we do get both
y^2 - 4xy + 4y = 1 and 3x^2 - 2xy = 1
The required solution of the equations is (1, 1)
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We'll change the first equation into:
y^2 + 4y = 4xy + 1
We'll change the 2nd equation into:
3x^2 = 2xy + 1
We'll re-write the first equation as:
y^2 + 4y = 2xy + 1 + 2xy
We'll substitute the sum 2xy + 1 by 3x^2:
y^2 + 4y = 3x^2 + 2xy
We notice that we'll substitute x and y by 1, we'll get:
1^2 + 4*1 = 3*1^2 + 2*1*1
1 + 4 = 3 + 2
5 = 5 true
The solution of the simultaneous equations is (1 ; 1), where x = 1 and y = 1.
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