Please provide solutions with detail explanations:

WORD PROBLEMS ON SYSTEMS OF LINEAR EQUATIONS (3X3 SYSTEMS)

1) Find the equation of the parabola y = ax + bx + c, that passes through the following three points: (-2, 40), (1, 7), (3, 15). Use the cramer's rule.

2) For the Summer Music Festival, there is one price for students, one for adults, and another for senior citizens. The Singh family bought 3 student tickets and 2 adult tickets for $104. The Kumar bought 5 student tickets, 1 adult ticket, and 2 senior citizen tickets for $155. The Browns bought 2 of each for $126.

a) Write a system of equations that can be used to find the cost of each ticket

b) Solve the system to find the cost of each ticket. Use the Cramer's rule

3) Use Gaussian Elimination to solve the linear system by finding an equivalent system in triangular form.

4x -2y +3z = 19

3x -2y -3z = -14

x -y + 5z = 24

4) Determine the quadratic function whose graph passes through the three given points: (0, 0 ) (-2, 14 ) (4, 20 ). Use the Gauss-Jordon (Gaussian) Elimination method.

Note:

After using appropriate E.R.Os and getting all 0s in the third row means that the system has INFINETLY MANY SOLUTIONS

i.e - - - -

- - - -

0 0 0 0

But if the RHS term is non-zero constant then the system is said to have NO solutions.

i.e - - - -

- - - -

0 0 0 k