maths, find two algebraic methods

Question

Four cousins who share the same birthday, David, Frederica, Mary and Laurent each receive a fish tank as a birthday present that contain two types of fish, swordtails and angelfish. There is a pamphlet with each tank regarding how many litres are required in a tank to keep the fish healthy.

The table below shows the number of fishes in each tank and the number of litres of water needed.

David: 3 sword fish | 4 angel fish | number of litres per tank = 24

Frederica: 4 swordfish | 6 angelfish | number of litres per tank = 35

Mary: 5 sword fish | 8 angel fish | number of litres per tank = ?

Laurent: 7 sword fish | ? angel fish | number of litres per tank = 63.5

Q: find the number of litres required by one swordfish and one angel fish by two different algebraic methods

Answer 1

Let's assume sword=x and angel=y

So first equation will be 3x+4y=24...(i)

Second will be 4x+6y=35...(ii)

Now,

Method 1:

Multiply the first equation with 3 and second equation with 2. Subtract second equation from one and get the value of x.Now put the value in any equation and get the value of y.

Method 2:

Get the value of x from first equation and put it in the second equation thus you'll get the original value of y.Now put the value of y in any equation and thus get the value of x.