Question

jelanie wrote the system of linear equations below to represent the number of student and adult tickets he and his friend sold to their school play 12s+10a=128 16s+21a=232 jelani also wrote the augmented sound matrix to represent this system which matrix could melanin have written

Answer 1

`\large\boxed{\left[\begin{array}{ccc}12&10&128\\16&21&232\end{array}\right] }`

Explanation:

`\left\{\begin{array}{ccc}ax+by=n\\cx+dy=m\end{array}\right\Rightarrow\left[\begin{array}{ccc}a&b&n\\c&d&m\end{array}\right]`

`\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}12s+10a=128\\16s+21a=232\end{array}\right\Rightarrow\left[\begin{array}{ccc}12&10&128\\16&21&232\end{array}\right]`

Answer 2

`\left[\begin{array}{ccc}12&10&|128\\16&21&|232\end{array}\right]`

Explanation:

The two equations Jelani wrote are:

12s+10a=128

16s+21a=232

The coefficient matrix is:

`\left[\begin{array}{cc}12&10\\16&21\end{array}\right]`

The constant matrix is:

`\binom{128}{232}`

The augmented matrix is the combination of the coefficient matrix and the constant matrix.

`\left[\begin{array}{ccc}12&10&|128\\16&21&|232\end{array}\right]`