Question

. MATHEMATICS: 1. Given that x + y =3/4 and x - y =5/2 find the value of 2y + x

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Answer 1

-1/8

Explanation:

x + y = 3/4

x -y = 5/2

2x = 13/4 3/4 + 5/2 = 3/4 + 10/4 = 13/4 Next divide both sides by 2

`(2x)/(2)` =
`((13)/(4) )/(2)`
`(13)/(4)` ÷
`(2)/(1)` =
`(13)/(4)` x
`(1)/(2)` =
`(13)/(8)`

x =
`(13)/(8)`

plug in 13/8 for x in either of the two original equations.

x + y = 3/4

13/8 + y = 3/4 Subtract 13/8 from both sides

y = -7/8 3/4 - 13/8 = 6/8 - 13/8 = -7/8

Check:

substitute x = 13/8 and y = -7/8 back into the original two equations to see if the equations ae true

x + y = 34

13/8 - 7/8 = 3/4

6/8 = 3/4

3/4 = 3/4 Checks

x - y = 5/2

13/8 - (-7/8) = 5/2

13/8 + 7/8 = 5/2

20/8 = 5/2

5/2 = 5/2 Checks

Find the value of 2y + x

2(-7/8) + 13/8

-14/8 + 13/8

-1/8

Answer 2

Explanation:

`x = (13)/(8) \\ y = ( - 7)/(8) \\ 2y + x = - (14)/(8) + (13)/(8) = - (1)/(8)`