Question

Which ordered pair (x, y) is a solution to given system of linear equations?

(3x+y = 1
15x+y = 3
O (-2, 1)
O (-0.5, 0.5)
0 (0.5, -0.5)
O (1, -2)

Answer 1

`((1)/(6), (1)/(2))` or
`(0.167,0.5)`

Explanation:

Given

`3x + y =1`

`15x + y = 3`

Required

Determine the solution

We'll solve using elimination method.

Subtract the first equation from the second:

`15x + y = 3`

`3x + y =1`

`--------`

`15x - 3x + y - y = 3 - 1`

`15x - 3x + y - y = 3 - 1`

`15x - 3x = 3 - 1`

`12x = 2`

Make x the subject:

`x = (2)/(12)`

`x = (1)/(6)`

`x =0.167`

Substitute
`(1)/(6)` for x in the first equation

`3x + y =1`

`3((1)/(6)) + y = 1`

`(1)/(2) + y = 1`

Make y the subject

`y = 1 -(1)/(2)`

`y = (2-1)/(2)`

`y = (1)/(2)`

`y = 0.5`

Hence, the solution is:

`((1)/(6), (1)/(2))` or
`(0.167,0.5)`