Question

Maya wrote the following matrix equation to represent a system of equations:

[4 8]*[x] = 0
[2 5] [y] = 6

What is the solution of the system?

Answer 1

I am somehow confused with the given matrix. Because usually, when the system of equations is given as:

ax + by = c
dx + ey = f

the matrix would be written in this manner:


`\left[\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right]`

Let me just assume that the arrangement of the given corresponds to this system of equations:

4x + 8y = 0
2x + 5y = 6

So you write it as


`\left[\begin{array}{ccc}4&8&0\\2&5&6\end{array}\right]`

In order to solve this, the matrix should look like this where x and y are the answers


`\left[\begin{array}{ccc}1&0&x\\0&1&y\end{array}\right]`


So, the first thing to do is apply this pattern: Row 2 = Row 1 - 2*Row 2. The result will be


`\left[\begin{array}{ccc}4&8&0\\0&-2&-12\end{array}\right]`

Next, Row 1 = (Row 1/4) + R2:


`\left[\begin{array}{ccc}1&0&-12\\0&-2&-12\end{array}\right]`

Lastly, Row 2 = Row 2 / -2:


`\left[\begin{array}{ccc}1&0&-12\\0&1&6\end{array}\right]`

Thus, the answer is x=-12 and y=6.