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

Use Cramer’s Rule to solve the system of linear equations.
$\left\{\begin{array}{l}20x+8y=11\\ 12x-24y=21\end{array}$

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Step 1
Given system of equations is
$\left\{\begin{array}{l}20x+8y=11\\ 12x-24y=21\end{array}$
Firstly, we evaluate the value of determinant of coefficient matrix
$D=|\begin{array}{cc}20& 8\\ 12& -24\end{array}|=20\left(-24\right)-12\left(8\right)=-576$
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.
${D}_{1}=|\begin{array}{cc}11& 8\\ 21& -24\end{array}|=11\left(-24\right)-21\left(8\right)=-432$
${D}_{2}=|\begin{array}{cc}20& 11\\ 12& 21\end{array}|=20\left(21\right)-12\left(11\right)=288$
Solution of given system of equations is
$x=\frac{{D}_{1}}{D},y=\frac{{D}_{2}}{D}$
$x=\frac{-432}{-576},y=\frac{288}{-576}$
$x=\frac{3}{4},y=-\frac{1}{2}$
Step 3
Result:
$x=\frac{4}{3}.y=-\frac{1}{2}$