Use Cramer’s Rule to solve the system of linear equations.20x+8y=1112x-24y=21

Step 1
Given system of equations is
$\{\begin{array}{l}20x+8y=11\\ 12x-24y=21\end{array}$
Firstly, we evaluate the value of determinant of coefficient matrix
${\displaystyle D=\left|\begin{array}{cc}20& 8\\ 12& -24\end{array}\right|=20(-24)-12\left(8\right)=-576}$
Since, the value of determinant of coefficient matrix is non-zero,
So, given system of equation is consistent.
Step 2
Now, we consider the following determinants.
${\displaystyle D_1=\left|\begin{array}{cc}11& 8\\ 21& -24\end{array}\right|=11(-24)-21\left(8\right)=-432}$
${\displaystyle D_2=\left|\begin{array}{cc}20& 11\\ 12& 21\end{array}\right|=20\left(21\right)-12\left(11\right)=288}$
Solution of given system of equations is
${\displaystyle x=\frac{D_1}{D},y=\frac{D_2}{D}}$
${\displaystyle x=\frac{-432}{-576},y=\frac{288}{-576}}$
${\displaystyle x=\frac{3}{4},y=-\frac{1}{2}}$
Step 3
Result:
${\displaystyle x=\frac{4}{3}.y=-\frac{1}{2}}$