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 )

Question

asked Jan 18, 2021 96.6k views

1 Answer

GeekzSG · Answer 1 · 2021-01-22T06:26:36+0000

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))