Question

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

Answer 1

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.

Step-by-step 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

$\frac{-2y}{-2}=\frac{-1}{-2}$

$y=\frac{1}{2}$

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

$x+\frac{1}{2}=3$

$x+\frac{1}{2}-\frac{1}{2}=3-\frac{1}{2}$

$x=\frac{5}{2}$

so

$x=\frac{5}{2},\:y=\frac{1}{2}$

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.