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(х+6y)^2=7y; (x+6y)^2=7x

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The solution

You have entered [src]
         2      
(x + 6*y)  = 7*y
$$\left(x + 6 y\right)^{2} = 7 y$$
         2      
(x + 6*y)  = 7*x
$$\left(x + 6 y\right)^{2} = 7 x$$
(x + 6*y)^2 = 7*x
Rapid solution
$$x_{1} = 0$$
=
$$0$$
=
0

$$y_{1} = 0$$
=
$$0$$
=
0
$$x_{2} = \frac{1}{7}$$
=
$$\frac{1}{7}$$
=
0.142857142857143

$$y_{2} = \frac{1}{7}$$
=
$$\frac{1}{7}$$
=
0.142857142857143
Numerical answer [src]
x1 = 0.1428571428571429
y1 = 0.1428571428571429
x2 = 0.1428571428598863
y2 = 0.1428571428598863
x3 = -2.434574337728793e-21
y3 = -2.434574337728854e-21
x4 = -1.28902045796802e-25
y4 = -1.289020457960262e-25
x5 = -4.903168451340711e-12
y5 = -4.903168451340711e-12
x6 = -2.968665246054741e-32
y6 = -2.968665269874573e-32
x7 = 0.1428571428571504
y7 = 0.1428571428571504
x8 = 0.142857142857143
y8 = 0.142857142857143
x9 = 0.1428571428573401
y9 = 0.1428571428573401
x9 = 0.1428571428573401
y9 = 0.1428571428573401