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Sagot :
Given,
The equations are
[tex]\begin{gathered} 4x-6y=-7..............(1) \\ -2x+3y=18............(2) \end{gathered}[/tex]To find: Does the following system have a unique solution? Why?
Solution:
The determinant of the given equations are
[tex]\begin{gathered} \begin{bmatrix}{4} & {-6} \\ {-2} & {3}\end{bmatrix}=\begin{bmatrix}{-7} & {} \\ {18} & {}\end{bmatrix} \\ 4\times3-(-6\times-2) \\ =12-12 \\ =0 \end{gathered}[/tex]For unique solutions, the condition is
[tex]\begin{gathered} \frac{a_1}{a_2}=\frac{b_1}{b_2} \\ \frac{4}{-2}=\frac{-6}{3} \\ -2=-2 \end{gathered}[/tex]Condition satisfied.
Hence, the given equations have a unique solution.
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