Equation1

Equation2

Equation3

Equation4

Use the Chinese Remainder Theorem.

However, for this question try this:

The values that satisfy Eqn4 are

4, 11, 18, 25, 32, 39, ...

They are 4 + multiples of 7.

Use those values in Eqn3

18 satisfies Eqn4 & Eqn3

Use 18 + multiples of 35 ( 7 times 5 ) for Equation2

18, 53, 88, 123, ...

Find the one that satisfies equation2.

Then a similar procedure for Equation1

.