We have the following:
the system of linear equations is
[tex]\begin{gathered} \frac{2}{5}x+\frac{1}{4}y=\frac{9}{20} \\ \frac{2}{3}x+\frac{5}{12}y=\frac{3}{4} \end{gathered}[/tex]now, using Cramer's rule
To solve for Cramer's rule the first thing is to calculate the determinant of the matrix
[tex]\begin{bmatrix}{a_{11}} & {a_{12}} & {} \\ {a_{21}} & {a_{22}} & \end{bmatrix}=a_{11}\cdot a_{22}-a_{12}\cdot a_{21}[/tex]replacing:
[tex]\begin{gathered} =\frac{2}{5}\cdot\frac{5}{12}-\frac{1}{4}\cdot\frac{2}{3} \\ =\frac{2}{12}-\frac{2}{12} \\ =0 \end{gathered}[/tex]