Respuesta :
we are given two system of equations
First equation is
[tex]y=2x-1[/tex]
we can write as
[tex]-2x+y=-1[/tex]
Second equation is
[tex]6x-y=13[/tex]
now, we can find augmented matrix
[tex]A=\begin{pmatrix}-2&1&-1\\ 6&-1&13\end{pmatrix}[/tex]
now, we can change it into reduced row echelon form
step-1: multiply the 1st row by -1/2
[tex]A=\begin{pmatrix}-1&-1/2&1/2\\ 6&-1&13\end{pmatrix}[/tex]
step-2: add -6 times the 1st row to the 2nd row
[tex]A=\begin{pmatrix}-1&-1/2&1/2\\ 0&2&10\end{pmatrix}[/tex]
step-3:multiply the 2nd row by 1/2
[tex]A=\begin{pmatrix}-1&-1/2&1/2\\ 0&1&5\end{pmatrix}[/tex]
step-4:add 1/2 times the 2nd row to the 1st row
[tex]A=\begin{pmatrix}1&0&3\\ 0&1&5\end{pmatrix}[/tex]
so, we will get
[tex]x=3,y=5[/tex]
Answer is (3,5)
