Hey guys, could someone help me with this system of equations?

Of course you're right, CPhill.

(1+ (6 (sqrt (2)) / 5 = (1+√72)/5

I do not correct, we have your right solution.
Thanks for the correction.   !

x^2+y^2 = 36

y = (1+ (6(sqrt(2))/5)x-6

\(x^2+y^2=36\)

\(y=(1+6\times \frac{\sqrt{2}}{5})x-6=2.69705627484x-6\)

\(y^2=7.27411254965x^2-32.3646752981x+36\)

\(x^2+7.27411254965x^2-32.3646752981x+36=36\)

\(8.27411254965x^2-32.3646752981x=0\)

\(x\times(8.27411254965x-32.3646752981)=0\)

\(x_1=0\)

\(y_1=\pm\sqrt{36}=\pm6\)  (+6 entfällt)

\(x_2= \frac{32.3646752981}{8.27411254965}\)

\(x_2=3.91155850297\)

\(y_2=\pm\sqrt{36-3.91155850297^2}\)

\(y_2=\pm4.54969340481\)   (-4.54969... entfällt)

  !

y = (1+ (6(sqrt(2))/5)x-6  

y =  ( [  1  + √72 ] / 5  )  x  -   6        

y^2 =   ( [  1  + √72 ]^2  / 25 ) x^2  - (12/5) [  1  + √72 ] x  + 36  =

(  [ 73  + 2√72] / 25 ) x^2    - (12/5) [  1  + √72 ] x  + 36

Put this back into  x^2  + y^2  = 36    for  y^2

x^2   +  (  [ 73  + 2√72] / 25 ) x^2    - (12/5) [  1  + √72 ] x  + 36   = 36

x^2  +  (  [ 73  + 2√72] / 25 ) x^2    - (12/5) [  1  + √72 ] x   =  0     factor

x  (   [ 1  +  [ 73  + 2√72] / 25) ] x    - (12/5) [  1  + √72 ] ) = 0     set each factor to  0

x  = 0     and

(   [ 1  + ( [ 73  + 2√72] / 25) ] x    - (12/5) [  1  + √72 ] )  = 0

[  [25 + 73  + 2√72] / 25] x  =  [ 12 [  1  + √72 ] ] / 5

[[ 98 +  2√72] / 25] x  = [ 12  + 12 √72]  / 5

[ (98 +  2√72) / 5] x  = [ 12  + 12 √72]

x  = 5* [ 12  + 12 √72]  / (98 +  2√72)   ≈   4.9501

Here's the graph  :  https://www.desmos.com/calculator/wjjz1t33v1

Asinus  and I  have interpreted this    (1+ (6(sqrt(2))/5)x   in two different ways.....thus... the different  results

[ WolframAlpha  says  that the parentheses/brackets are mismatched......so   what was intended is hard to determine  ]

Choose your poison wisely.....

\(x²+[ (1+\frac{6\sqrt2}{5})x-6]² = 36\)

\(x²+ (1+\frac{6\sqrt2}{5})²x²-12x(1+\frac{6\sqrt2}{5})+36 = 36\)

\(x[(1+ (1+\frac{6\sqrt2}{5})²)x-12(1+\frac{6\sqrt2}{5}) ]= 0\)

so: x=0 and \((1+ (1+\frac{6\sqrt2}{5})²)x-12(1+\frac{6\sqrt2}{5}) = 0\)

\( x =\frac{12(1+\frac{6\sqrt2}{5})}{(1+ (1+\frac{6\sqrt2}{5})²)}\)

\( x =\frac{12(1+\frac{6\sqrt2}{5})}{1+ 1+\frac{72}{25}+\frac{12\sqrt2}{5}}\)

\( x ={\frac{300+360\sqrt2}{122+60\sqrt2}}\)

\(x=3.91\)

Thanks, Majid.....I suspect your answer is the one wanted.....

Thanks a lot :D