Question

Solve the system of linear equations using matricesX + 6y=7x + 5y=4

Answer 1

Using matrices, the system would be

`\begin{bmatrix}{1} & {6} & {7} \\ {1} & {5} & {4}\end{bmatrix}`

We just have to make zero the second 1 of the first column. To do that, we subtract the first row with the second row.

`\begin{bmatrix}{1} & 6 & {7} \\ {0} & {1} & {3} \\ {} & {} & {}\end{bmatrix}`

Since 1-1=0, 6-5=1, and 7-4=3.

Now we transform the matrices in equations again.

`\begin{gathered} x+6y=7 \\ 0x+y=3 \end{gathered}`

As you can observe, we already got y=3. We use this value to find x

`\begin{gathered} x+6(3)=7 \\ x+18=7 \\ x=7-18=-11 \end{gathered}`

Therefore, the solutions are y=3 and x=-11.