Question

An education fund allocates RM10,000 to help 100 students from form three, form five and form six in a school. Each form three student receives RM80, each form five student receives RM120 and each form six student receives RM160. The number of form three students that receive the aid is twice the number of form five students.
(a) Form a system of linear equations from the above information.
(b) Hence, determine the number of students for each form that receive the aid by using matrices.

Answer 1

Form three students --- x
form five students ---- y
form six students ----- 100-x-y

80x + 120y + 160(100-x-y) = 10000
80x + 120y + 16000-160x-160y = 10000
-80x - 40y = -6000
2x + y = 150

but it said:
x = 2y
2(2y) + y = 150
y = 30
x = 2y = 60
remaining students = 100-30-60 = 10

I did not use matrices on such a simple problem because solving it was so much easier using the above method,
but.... if you have to use matrices

our two equations are:
2x + y = 150
x - 2y = 0

2 1 150
1 -2 0 ---->

4 2 300
1 -2 0 --->

1 -2 0
4 2 300 ---> add

1 -2 0
5 0 300

1 -2 0
1 0 60

from the last x=60
in 1st: 60-2y=0
-2y=-60
y=30
etc