can we solve these equations manually? how can we find the values for x?
No, it can't be solved algebraically because we have an x as the exponent in the first equation and as a base in the second
. Let and the graphs will be equal where they intersect, thus
Since the root is between (if you were to do this on pen and paper then you'd use an iterative solution converging on x)
Out of personal interest how would you know this particular system has two real solutions?