Step 1

Given system of equations is

20x+8y=11

12x-24y=21

Firstly, we evaluate the value of determinant of coefficient matrix

\(\displaystyle{D}={\left|\begin{array}{cc} {20}&{8}\\{12}&-{24}\end{array}\right|}={20}{\left(-{24}\right)}-{12}{\left({8}\right)}=-{576}\)

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.

\(\displaystyle{D}_{{1}}={\left|\begin{array}{cc} {11}&{8}\\{21}&-{24}\end{array}\right|}={11}{\left(-{24}\right)}-{21}{\left({8}\right)}=-{432}\)

\(\displaystyle{D}_{{2}}={\left|\begin{array}{cc} {20}&{11}\\{12}&{21}\end{array}\right|}={20}{\left({21}\right)}-{12}{\left({11}\right)}={288}\)

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:

\(\displaystyle{x}=\frac{{4}}{{3}}.{y}=-\frac{{1}}{{2}}\)

Given system of equations is

20x+8y=11

12x-24y=21

Firstly, we evaluate the value of determinant of coefficient matrix

\(\displaystyle{D}={\left|\begin{array}{cc} {20}&{8}\\{12}&-{24}\end{array}\right|}={20}{\left(-{24}\right)}-{12}{\left({8}\right)}=-{576}\)

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.

\(\displaystyle{D}_{{1}}={\left|\begin{array}{cc} {11}&{8}\\{21}&-{24}\end{array}\right|}={11}{\left(-{24}\right)}-{21}{\left({8}\right)}=-{432}\)

\(\displaystyle{D}_{{2}}={\left|\begin{array}{cc} {20}&{11}\\{12}&{21}\end{array}\right|}={20}{\left({21}\right)}-{12}{\left({11}\right)}={288}\)

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:

\(\displaystyle{x}=\frac{{4}}{{3}}.{y}=-\frac{{1}}{{2}}\)