Question

Question 9

Solve the following system of equations using matrices.
y = 2x – 1
6x – y = 13

(3, 5)

(-3, 5)

(5, 0)

Answer 1

-3 and 5 are the answer

Answer 2

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)