# Solve the system of linear equations using determinants: 3x+2y=2 x+4y=1Show step by step process to explain the solution and answer.

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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:**