Answer: he works 37 hours in job A, and 22 hours in job B.
Step-by-step explanation:
Let's define the variables:
A = number of hours that he works at Job A
B = number of hours that he works at Job B.
We know that he works a total of 59hr per week, then we have:
A + B = 59
And we also know that he makes $494 in one week, then we have the equation:
A*$8 + B*$9 = $494.
Then we have the system of equations:
A + B = 59
A*$8 + B*$9 = $494
To solve this with an augmented matrix, we need to turn these equations into a matrix, where we only write the coefficients as follows:
[tex]\left[\begin{array}{cccc}1&1&I&59\\8&9&I&494\end{array}\right][/tex]
(The I's should represent a line for the augmented matrix, that line separates the values of the coefficients to the right value of each equation)
The first column represents the A coefficients, the second column represents the B coefficients.
To solve this, we want to get something of the form:
[tex]\left[\begin{array}{cccc}1&0&I&x\\0&1&I&y\end{array}\right][/tex]
Where x and y are our solutions.
To do it we can just do: Column 2 - 8*column 1, this will get us to:
[tex]\left[\begin{array}{cccc}1&1&I&59\\8 - 8*1&9 - 8*1&I&494 - 8*59\end{array}\right][/tex]
=
[tex]\left[\begin{array}{cccc}1&1&I&59\\0&1&I&22\end{array}\right][/tex]
Now we can do: Column1 - column2, to get
[tex]\left[\begin{array}{cccc}1 - 0&1 - 1&I&59 - 22\\0&1&I&22\end{array}\right][/tex]
[tex]\left[\begin{array}{cccc}1&0&I&37\\0&1&I&22\end{array}\right][/tex]
Then the solutions are:
1*A =37
1*B = 22
This means that he works 37 hours in job A, and 22 hours in job B.
