Step 1

Consider the following system of linear equations:

2x+y=-10

6x−3y=6

Rewrite the system in the form of augmented matrix:

\(\displaystyle{\left[\begin{array}{cc|c} {2}&{1}&-{10}\\{6}&-{3}&{6}\end{array}\right]}\)

\(\displaystyle{R}_{{1}}\rightarrow\frac{{1}}{{2}}{R}_{{1}}\)

\(\displaystyle{\left[\begin{array}{cc|c} {1}&\frac{{1}}{{2}}&-{5}\\{6}&-{3}&{6}\end{array}\right]}\)

Step 2

\(\displaystyle{R}_{{2}}\rightarrow{R}_{{2}}-{6}{R}_{{1}}\)

\(\displaystyle{\left[\begin{array}{cc|c} {2}&\frac{{1}}{{2}}&-{5}\\{0}&-{6}&{36}\end{array}\right]}\)

\(\displaystyle{R}_{{2}}\rightarrow\frac{{-{1}}}{{6}}{R}_{{2}}\)

\(\displaystyle{\left[\begin{array}{cc|c} {1}&\frac{{1}}{{2}}&-{5}\\{0}&{1}&-{6}\end{array}\right]}\)

Step 3

\(\displaystyle{R}_{{1}}\rightarrow{R}_{{1}}-\frac{{1}}{{2}}{R}_{{2}}\)

\(\displaystyle{\left[\begin{array}{cc|c} {1}&{0}&-{2}\\{0}&{1}&-{6}\end{array}\right]}\)

x=−2

y=−6

Hence, the solution is x=−2 and y=−6.

Consider the following system of linear equations:

2x+y=-10

6x−3y=6

Rewrite the system in the form of augmented matrix:

\(\displaystyle{\left[\begin{array}{cc|c} {2}&{1}&-{10}\\{6}&-{3}&{6}\end{array}\right]}\)

\(\displaystyle{R}_{{1}}\rightarrow\frac{{1}}{{2}}{R}_{{1}}\)

\(\displaystyle{\left[\begin{array}{cc|c} {1}&\frac{{1}}{{2}}&-{5}\\{6}&-{3}&{6}\end{array}\right]}\)

Step 2

\(\displaystyle{R}_{{2}}\rightarrow{R}_{{2}}-{6}{R}_{{1}}\)

\(\displaystyle{\left[\begin{array}{cc|c} {2}&\frac{{1}}{{2}}&-{5}\\{0}&-{6}&{36}\end{array}\right]}\)

\(\displaystyle{R}_{{2}}\rightarrow\frac{{-{1}}}{{6}}{R}_{{2}}\)

\(\displaystyle{\left[\begin{array}{cc|c} {1}&\frac{{1}}{{2}}&-{5}\\{0}&{1}&-{6}\end{array}\right]}\)

Step 3

\(\displaystyle{R}_{{1}}\rightarrow{R}_{{1}}-\frac{{1}}{{2}}{R}_{{2}}\)

\(\displaystyle{\left[\begin{array}{cc|c} {1}&{0}&-{2}\\{0}&{1}&-{6}\end{array}\right]}\)

x=−2

y=−6

Hence, the solution is x=−2 and y=−6.