Show that x + y : x - y= 3 : 2

Question

asked Apr 18, 2021 109k views

1 Answer

Seabass · Answer 1 · 2021-04-25T13:53:07+0000

Answer:

x + y : x - y = (5/2+1/2) : (5/2-1/2)

x + y : x - y = 3 : 2

Therefore, x + y : x - y= 3 : 2 is proved.

Explanation:

Given

x + y : x - y = 3 : 2

As

x + y = 3

x - y = 2

Solving to find x and y

$\begin{bmatrix}x+y=3\\ x-y=2\end{bmatrix}$

x-y=2

$\underline{x+y=3}$

-2y=-1

$\begin{bmatrix}x+y=3\\ -2y=-1\end{bmatrix}$

solve for y

-2y=-1

Divide both sides by 2

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

y=(1)/(2)

$\mathrm{For\:}x+y=3\mathrm{\:plug\:in\:}y=(1)/(2)$

x+(1)/(2)=3

x+(1)/(2)-(1)/(2)=3-(1)/(2)

x=(5)/(2)

so

$x=(5)/(2),\:y=(1)/(2)$

Thus,

x + y : x - y = (5/2+1/2) : (5/2-1/2)

x + y : x - y = 3 : 2

Therefore, x + y : x - y= 3 : 2 is proved.