Question

Use matrix method to solve x+4y=8 2x+y=9

Answer 1

In first equation, x has coefficient 1 and y has coefficient 4 and is equal to 8
In first equation, x has coefficient 2 and y has coefficient 1 and is equal to 9

So augmented matrix would looks like this:

`\left[\begin{array}c1&4&8\\2&1&9\end{array}\right]`

Your goal is to transform matrix to look like this:

`\left[\begin{array}cc1&0&x_{\text{answer}}\\0&1&y_{\text{answer}}\end{array}\right]`

Steps to reach there:

Subtract first row from second row two times:

`\left[\begin{array}cc1&4&8\\0&-7&-7\end{array}\right]`

Multiple second row by -1/7:

`\left[\begin{array}c1&4&8\\0&1&1\end{array}\right]`

Now subtract second row from first row 4 times:


`\boxed{\left[\begin{array}c1&0&4\\0&1&1\end{array}\right]}`

Which translate to

`x+0y = 4\\\ \\0x+y=1`

So then x = 4 and y = 1.

Hope this helps.