Correct Answer - Option 3 : unique solution
Concept:
Let us consider the system of linear equations:
a11 × x + a12 × y = b1
a21 × x + a22 × y = b2
We can write these equations in matrix form as: A X = B,
where \(A = \left[ {\begin{array}{*{20}{c}} {{a_{11}}}&{{a_{12}}}\\ {{a_{21}}}&{{a_{22}}} \end{array}} \right],\;X = \left[ {\begin{array}{*{20}{c}} x\\ y \end{array}} \right]\;and\;B = \left[ {\begin{array}{*{20}{c}} {{b_1}}\\ {{b_2}} \end{array}} \right]\)
In order to say that the given system of linear equations is consistent and has a unique solution, |A| ≠ 0.
Analysis:
89x + 37y = -7
87x + 74y = -5
\(A = \left[ {\begin{array}{*{20}{c}} {29}&{37} \\ {87}&{74} \end{array}} \right]\;\;\;B = \left[ {\begin{array}{*{20}{c}} { - 7} \\ { - 5} \end{array}} \right]\)
|A| = 29 × 74 – 87 × 37
= -1073 ≠ 0
∴ Solution is unique
