Question

using Cramer's rule what is the value of x in the solution to the system of linear equations below?2/5x+1/4y=9/202/3x+5/12y=3/4

Answer 1

We have the following:

the system of linear equations is

$\begin{gathered} \frac{2}{5}x+\frac{1}{4}y=\frac{9}{20} \\ \frac{2}{3}x+\frac{5}{12}y=\frac{3}{4} \end{gathered}$

now, using Cramer's rule

To solve for Cramer's rule the first thing is to calculate the determinant of the matrix

$\begin{bmatrix}{a_{11}} & {a_{12}} & {} \\ {a_{21}} & {a_{22}} & \end{bmatrix}=a_{11}\cdot a_{22}-a_{12}\cdot a_{21}$

replacing:

$\begin{gathered} =\frac{2}{5}\cdot\frac{5}{12}-\frac{1}{4}\cdot\frac{2}{3} \\ =\frac{2}{12}-\frac{2}{12} \\ =0 \end{gathered}$