Question

Which ordered pair is a solution of linear equations?

Answer 1

`\{(2)/(3), (1)/(5)\}`

ordered pair is the Solution to the given System.

Explanation:

Given:

`(1)/(2)x- (3)/(4)y= (11)/(60) ...........Equation( 1 )\\ \\(2)/(5)x+ (1)/(6)y= (3)/(10) ...........Equation( 2 )\\`

To Check:

Which ordered pair is the Solution to the given System. ?

Solution:

If
`\{(2)/(3), (1)/(5)\}`

is the Solution then it must satisfy the given equation. i.e .Left Hand Side (L.H.S) must be Equal to Right Hand Side (R.H.S) of both the given equation for

`\{x=(2)/(3), y=(1)/(5)\}`

∴ For Equation ( 1 )

`L.H.S=(1)/(2)* (2)/(3)- (3)/(4)* (1)/(5)\\\\\\=(1)/(3) -(3)/(20) \\\\=(20-9)/(20* 3)\\\\ =(11)/(60) \\= R.H.S`

∴ Left Hand Side = Right Hand Side

Hence,

`\{x=(2)/(3), y=(1)/(5)\}`

The solution.

∴ For Equation ( 2 )

`L.H.S=(2)/(5)* (2)/(3)+ (1)/(6)* (1)/(5)\\\\\\=(4)/(15) -(1)/(30) \\\\=(120+15)/(15* 30)\\\\= (135)/(450)\\ \\\\=(3)/(30)\\ \\= R.H.S`

∴ Left Hand Side = Right Hand Side

Hence ,

`\{x=(2)/(3), y=(1)/(5)\}`

The solution.

For other Solutions we do not have Left Hand Side equal to Right Hand Side.

i.e Left Hand Side ≠ Right Hand Side

Hence Not a Solution.