Question

Solve the system. 2(y - x) = 5 + 2x 2(y + x) = 5 - 2y A) ( 1 2 , 3 2 ) B) (−2, 2 3 ) C) (− 1 2 , 3 2 ) D) ( 1 2 , − 3 2 )

Answer 1

Answer: C)
`(-(1)/(2),(3)/(2))`

Explanation:

The given system of equations :

`2(y-x) = 5+2x\ \ ...(i)\\\\ 2(y+x)=5-2y\ \ ..(ii)`

Simplify left side, we get

`2y-2x=5+2x\Rightarrow\ 2y-4x=5\ \ ...(iii)\\\\ 2y+2x=5-2y\Rightarrow\ 4y+2x=5\ \ ...(iv)`

Multiplying 2 on equation (iii), we get

`4y-8x=10\ \ ...(v)`

Subtracting (v) from (iv) , we get

`2x-(-8x)=5-10\\\\\Rightarrow\ 2x+8x=-5\\\\\Rightarrow\ 10x=-5\\\\\Rightarrow\ x=-(5)/(10)=-(1)/(2)`

Put value of
`x=-(1)/(2)` in (v), we get

`4y-8(-(1)/(2))=10\\\\\Rightarrow \ 4y+4=10\\\\\Rightarrow\ 4y=10-4=6\\\\\Rightarrow\ y=(6)/(4)=(3)/(2)`

hence, the solution to the system is
`(x,y)=(-(1)/(2),(3)/(2))`