Solve the system of linear equations using determinants:
Show step by step process to explain the solution and answer.
1 Answer | Add Yours
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,
|c d| = (ad-bc) = D
Cramer's Rule says that,
If Dy is the deteminant
|c e'| = ae'-ce
and Dx is the determinant,
|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`
`y = (Dy)/D =1/10 = 0.1`
The soultions are x=0.6 and y=0.1.
Join to answer this question
Join a community of thousands of dedicated teachers and students.Join eNotes