Use row operations to solve a system with two Equations

Use row operations to solve a system with two Equations

 

Row operations can be used to rewrite a matrix. The goal is a matrix in the form

\begin{bmatrix}  1 & a& \left.\begin{matrix}  &  & \\  &  &  \end{matrix}\right|b\\  0& 1 & \left.\begin{matrix}  &  & \\  &  &  \end{matrix}\right|c  \end{bmatrix}.

 

for systems with  equations, respectively. Notice that there are 1s down the diagonal from upper left to lower right and 0s below the 1s. A matrix written this way is said to be in row echelon form. When these matrices are rewritten as systems of equations, the value of one variable is known, and the rest can be found by substitution. The following examples illustrate this method.

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