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Solve the system of linear equations using determinants: 3x+2y=2 x+4y=1Show step by...

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spock1 | Student, Undergraduate | Honors

Posted May 16, 2012 at 6:18 AM via web

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Solve the system of linear equations using determinants:

3x+2y=2

x+4y=1

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thilina-g | College Teacher | (Level 1) Educator

Posted May 16, 2012 at 6:49 AM (Answer #1)

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The determinant method is the same as Cramer's Rule.

If the two simultaneous equations are,

`ax+by = e `      and

`cx+dy = e'`

The determinant, D of the matrix is given by,

|a b|

|c d|    = (ad-bc) = D

Cramer's Rule says that,

If Dy is the deteminant

|a e|

|c e'|  = ae'-ce

and Dx is the determinant,

|e b|

|e' d|   = ed - be'

 

Then the solutions of the two equatiosn are given by,

x = Dx/D

and y = Dy/D

 

Therefore in our case, the equations are,

`3x+2y = 2 `      and

`x+4y = 1`

D = (3(4)-(2)1) = 10

Dx = (2(4)-2(1)) = 6

Dy = (3(1)-2(1)) = 1

 

Therefore according to Cramer's Rule,

`x = (Dx)/D = 6/10 = 0.6`

and,

`y = (Dy)/D =1/10 = 0.1`

 

The soultions are x=0.6 and y=0.1.

 

Sources:

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