Question

5x+y=-40
2x-5y=11
Cramer’s Rule
Help please

Answer 1

x=
`(211)/(27)`

Y=
`(25)/(27)`

Explanation:

For solving the two variable linear equation by Cramer's rule we have to find the determinant .

here, determinant D =
`\left[\begin{array}{ccc}5&1\\2&-5\\\end{array}\right]`

D=(5 × (-5)) - (2 × 1)

D = (-25)-(2)

D= -27

Now again we have to find the determinant with sub X and determinant with sub Y

Determinant with sub X ( Dx)

Dx=
`\left[\begin{array}{ccc}40&1\\11&-5\\\end{array}\right]`

Dx= ((40×(-5)) - (11×1)

Dx= -200-11

Dx= -211

now Determinant with sub Y Dy

Dy=
`\left[\begin{array}{ccc}5&40\\2&11\\\end{array}\right]`

Dy=(5×11)-(2×40)

Dy=(55-80)

Dy=-25

now to find the values of variables X and Y, we have to write

X=
`(Dx)/(D)`

or X=
`(-211)/(-27)`

and

Y=
`(Dy)/(D)`

i.e Y=
`(-25)/(-27)`

form here we got the value of variable X and Y (Answer)