# System of equations. Use matrices to solve 2x+y=-10 6x-3y=6

Question
Equations
System of equations. Use matrices to solve
2x+y=-10
6x-3y=6

2020-10-21
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.

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