Question

Which ordered pair is a solution to the system of linear equations 1/2x-3/4y=11/60 and 2/5x+1/6y=3/10

Answer 1

d

Explanation:

2/3, 1/5

Answer 2

`( (2)/(3) , (1)/(5) )`

EXPLANATION

The first equation is

`(1)/(2) x - (3)/(4) y = (11)/(60) ...(1)`

The second equation is

`(2)/(5) x + (1)/(6) y = (3)/(10) ...(2)`

We want to eliminate y, so we multiply the first equation by

`(4)/(5)`

`(4)/(5) * (1)/(2) x - (4)/(5) * (3)/(4) y = (11)/(60) * (4)/(5)`

`(2)/(5) x - (3)/(5) y = (11)/(75) ...(3)`

We now subtract equation (3) from (2)

`((2)/(3) x - (2)/(3) x )+ ( (1)/(6) y - - (3)/(5)y ) =( (3)/(10) - (11)/(75) )`

`(1)/(6) y + (3)/(5)y =(3)/(10) - (11)/(75)`

`(23)/(30)y = (23)/(150)`

Multiply both sides by

`(30)/(23)`

`\implies \: (30)/(23) * (23)/(30)y= (23)/(150) * (30)/(23)`

`\implies \: y = (1)/(5)`

Substitute into the first equation to solve for x .

`(1)/(2) x - (3)/(4) * (1)/(5) = (11)/(60)`

Multiply to obtain

`(1)/(2) x - (3)/(20) = (11)/(60)`

`(1)/(2) x = (11)/(60) + (3)/(20)`

`(1)/(2) x = (1)/(3)`

Multiply both sides by 2.

`2 * (1)/(2) x =2 * (1)/(3)`

`x = (2)/(3)`

The solution is

`( (2)/(3) , (1)/(5) )`