Ataxi travels for x hours at 80 km per hour (km/h) and y hours at
100 km/h. the average speed for the journey of 560 km is 93 km/h.
find x and y

We have to find two equations because we are working with two variables.

Equation 1: 80x+100y=560 (we know this because speed times time equals distance)

Equation 2: x+y=560/93 (we know this because total distance over total time is average speed)

Let us solve the system of equations by substitution.

x+y=560/93 ---> x=560/93-y

80x+100y=560

80(560/93-y)+100y=560

y=3.91 hours approx.

Now we can plug in x to solve for y.

x+3.91=560/93

x=2.11 hours approx.

x=2.11 hours approx. and y=3.91 hours approx.