Question

Question 9

Answer 1

we are given two system of equations

First equation is

$y=2x-1$

we can write as

$-2x+y=-1$

Second equation is

$6x-y=13$

now, we can find augmented matrix

$A=\begin{pmatrix}-2&1&-1\\ 6&-1&13\end{pmatrix}$

now, we can change it into reduced row echelon form

step-1: multiply the 1st row by -1/2

$A=\begin{pmatrix}-1&-1/2&1/2\\ 6&-1&13\end{pmatrix}$

step-2: add -6 times the 1st row to the 2nd row

$A=\begin{pmatrix}-1&-1/2&1/2\\ 0&2&10\end{pmatrix}$

step-3:multiply the 2nd row by 1/2

$A=\begin{pmatrix}-1&-1/2&1/2\\ 0&1&5\end{pmatrix}$

step-4:add 1/2 times the 2nd row to the 1st row

$A=\begin{pmatrix}1&0&3\\ 0&1&5\end{pmatrix}$

so, we will get

$x=3,y=5$

Answer is (3,5)

Answer 2

-3 and 5 are the answer