Situation $3.$ Solution to System of Linear Equation $(30$ ptis $)$

A civil engineering team is tasked with designing a new water distribution system network to supply water to three new

neighborhoods: $A,B,$ and C $.$ The water distribution network is to be designed with the following oriteria in mind:

Twice the neighborhood A requires $45$ itters per second $($Us$)$ more than neighborhood $C.$

The total demand for neighborhood A and twice the neighborhood $B$ together is $120$ liters per second $($U$/$s$)$

Neighborhood C requires a third of the water required by neighborhoods A and B combined.

The engineering team needs to calculate the water dernand for each neighborhood to ensure the distribution network meets

these requirements efficiently and without waste. To solve this problem, you need to assign:

The water demand for neighborhoods $A$ as $x(\frac{L}{s})$

The water dermand for neighborhoods $B$ as $y(\frac{L}{s})$

The water dernand for neighborhoods C as $z(\frac{L}{s})$

Then provide a system of linear equations using the criteria given above, you can form $3$ equations and $3$ uninowns. Using

any iterative methoda for solving the solution of linear equations, solve for the demands of neighborhoods $A,B,$ and C in

$(\frac{L}{s})$ Perform $7$ iterations.