Then the first equation says: a mother is 7 times as old as her son so:
y = 7x
Pretty straight forward.
And the second equation says: In five years time she will be 4 times her son's age.
This one takes a little more thought. if she is y years old now, then she will be y+5 years old in 5 years. So the LHS (left hand side) becomes y+5. And at that time she will be 4 times as old as her son, so the RHS becomes 4x. However, her son must have also aged 5 years, so x needs to be replaced with (x+5) and thus 4x becomes 4(x+5)
y+5 = 4(x+5)
Now we have two equations, lets substitute the top equation into the bottom equation:
y+5 = 4(x+5) becomes 7x+5 = 4(x+5)
Now we can distribute the 4 on the RHS
7x+5 = 4x+20
subtract 4x and subtract 5
3x = 15
divide by 3
x = 5
So we know that the son is 5 years old now. Lets substitute this value back into either equation to get a value for y. I'll do the top one since it is a simpler equation:
So the mother is 35 years old, and the son is 5 years old.
To check our work, we can see that she is 7 times as old as he is, and that in 5 years she will be 40 and he will be 10, and at that time she will be 4 times as old as he is. So we know we did it correctly.