Question

Write the augmented matrix for the following system of equations. -1+y=02 + 7x = -8y

Answer 1

The system of equations we have is

`\mleft\{\begin{aligned}-1+y=0 \\ 2+7x=-8y\end{aligned}\mright.`

Now, to find the aumented matrix, we have to have all of the variables in each equation on one side, for this in the first equation we add 1 to both sides of the equation:

`\begin{gathered} -1+y=0 \\ -1+1+y=0 \\ y=1 \end{gathered}`

And for the second equation we need to add 8y to both sides and substract 2 from both sides (this is to have variables on the left and independent number on the right):

`\begin{gathered} 2+7x=-8y \\ 7x+8y=-2 \end{gathered}`

Now, the system is left as follows

`\mleft\{\begin{aligned}y=1 \\ 7x+8y=-2\end{aligned}\mright.`

We represent this a matrix with the following form:

The first line will represent the first equation

The second line will represent the second equation

And the first column will be the x values, and the second column the y values:

`\begin{bmatrix}{0} & {1} & {1} \\ {7} & {8} & {-2}{}\end{bmatrix}`

I will expand on the meaning of this in the following diagram:

That last one is the aumented matrix of the system.