(a) The solution to the system of equation is, x = (d + b)/(ad - cb) and y = (-a - c)/(ad - cb).
(b) The condition at which the solution exists is, ad - cb ≠ 0.
<h3>
Solving the system of equation with Cramer's rule</h3>
ax + by = 1
cx + dy = -1
D = [a b]
[c d]
D = ad - cb
Dx = [1 b]
[-1 d]
Dx = d + b
Dy = [a 1]
[c - 1]
Dy = -a - c
x = Dx/D
x = (d + b)/(ad - cb)
y = Dy/D
y = (-a - c)/(ad - cb)
Cramer's rule applies to the case where the coefficient determinant is nonzero.
Thus, D ≠ 0 (ad - cb ≠ 0).
Learn more about Cramer's rule here: brainly.com/question/10445102
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