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December 20, 2014

December 20, 2014

Posted by **kchik** on Thursday, November 29, 2012 at 6:27am.

(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.

- basic math -
**Reiny**, Thursday, November 29, 2012 at 8:29amForm 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

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