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Answer :
Given the information on the problem, we can write the following system of equations:
[tex]\begin{cases}x+y=5 \\ 5x+7.5y=35\end{cases}[/tex]then, we can write the following augmented matrix:
[tex]\begin{bmatrix}{1} & {1} & {5} \\ {5} & {7.5} & {35}\end{bmatrix}[/tex]now, if we multiply by 5 the first row and then substract it from the second row, we get:
[tex]\begin{bmatrix}{1} & 1{} & {5} \\ {5} & {}7.5 & 35{}{}\end{bmatrix}\rightarrow\begin{bmatrix}{1} & 1{} & 5{} \\ {0} & {2.5} & {10}{}\end{bmatrix}[/tex]notice that from the second equation, we can find the value of y:
[tex]\begin{gathered} 2.5y=10 \\ \Rightarrow y=\frac{10}{2.5}=4 \\ y=4 \end{gathered}[/tex]now that we have that y = 4, we can use this value on the first equation to find x:
[tex]\begin{gathered} x+4=5 \\ \Rightarrow x=5-4=1 \\ x=1 \end{gathered}[/tex]now, we have that the babysitter worked 1 hour before 11pm and 4 hours after 11 pm,then, the Burkes came home at 3 am
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