I'm getting x = 9.3223 which rounds to 9.32. Nice work.
Once you know the value of x, you can use the law of sines to find the value of y
sin(A)/a = sin(B)/b
sin(y)/7 = sin(70)/x
sin(y)/7 = sin(70)/9.3223
sin(y) = 7*(sin(70)/9.3223)
sin(y) = 0.70560358983312
y = arcsin(0.70560358983312)
y = 44.8783278056846
y = 44.88 approximately
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If you must use the law of cosines, then here's how you could do it
c^2 = a^2 + b^2 - 2*a*b*cos(C)
7^2 = x^2 + 9^2 - 2*x*9*cos(y)
7^2 = (9.3223)^2 + 9^2 - 2*9.3223*9*cos(y)
49 = 86.90527729+81-167.8014cos(y)
49 = 167.90527729-167.8014cos(y)
-167.8014cos(y) = 49-167.90527729
-167.8014cos(y) = -118.90527729
cos(y) = -118.90527729/(-167.8014)
cos(y) = 0.708607182598
y = arccos(0.708607182598)
y = 44.8782954209662 ... this is slightly different from before due to rounding error
y = 44.88 approximately