If a plane can travel 520 miles per hour with the wind and 420 miles per hour against the wind, find the speed of the plane without a wind and the speed of the wind.

X=speed of the plane
y=speed of the wind.
we can suggest this system of equations:

x+y=520
x-y=420

we can solve this system of equations by reduction method.

x+y=520
x-y=420

2x=940                   ⇒x=940/2=470

    x+y=520
-1(x-y=420)

     2y=100              ⇒y=100/2=50

the speed of the plane is 470 miles/hour and the speed of the wind is 50 miles/hour.

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It’s hard to understand what you put.. can you show a picture ?