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For overdetermined systems, you can get solutions by explicitly specifying all variables:
var('k a x')
show(solve([a==-x, k*a^2==x^2], [k, a, x]))
The result is
[[k == 1, a == r1, x == -r1], [k == r2, a == 0, x == 0]]
where r1 and r2 are arbitrary parameters.
