Concept:A system of linear equations AX=B has a unique solution if det(A)=0.Explanation:Write the equations in matrix form:A=125215339, B=124.Compute det(A) by expanding along the first row:1⋅(1⋅9−3⋅5)−2⋅(2⋅9−3⋅5)+3⋅(2⋅5−1⋅5).Simplify each term:1(9−15)=−6,−2(18−15)=−6,+3(10−5)=15.Thus det(A)=−6−6+15=3=0.Since the determinant is non-zero, the system is consistent and has a unique solution.Answer:Option A: have a unique solution.