Answer:
Equivalent systems of equations review
Step-by-step explanation:
We're given two systems of equations and asked if they're equivalent.
x + 4y = 8 (1)
4x + y = 2 (2)
Interestingly, if we sum the equations in System A, we get:
Replacing the first equation in System A with this new equation, we get a system that's equivalent to System A:
This is System B, which means that System A is equivalent to System B.
Answer:
Rate of plane in still air = 1120 km/h
Rate of wind = 180 km/h
Step-by-step explanation:
Let the rate (speed) of the plane in still air = u km/h
Let the rate (speed) of the wind = v km/h
Formula for speed is:
Given that against the wind, airplane travels 7520 km in 8 hours.
The speed against the wind will be slower so,
Against the wind, speed = (u -v ) km/h
Using above formula:
Given that with the wind, airplane travels 6500 km in 5 hours.
The speed with the wind will be faster so,
With the wind, speed = (u +v ) km/h
Using above formula:
Adding (1) and (2) to solve for u and v:
Putting u in (1):
So, the answers are:
<em>Rate of plane in still air = 1120 km/h</em>
<em>Rate of wind = 180 km/h</em>
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