Aparticular computer takes 43 nanoseconds to carry out five sums and seven products. it takes 36 nanoseconds to carry out four sums and six products. how long does the computer take to carry out one sum? to carry out one product?

This is the concept of simultaneous equations:
Let the time taken to do one sum be x and time taken to do one product be y.
Total time taken to do 5 sums and seven products will be:
5x+7y=43

Total time taken to do 4 sums and 6 products will be:
4x+6y=36

This gives us the simultaneous equations:
5x+7y=43
4x+6y=36

multiply the top equation by 4 and the bottom equation by 5 then subtract the bottom equation from the top gives us:
-2y=-8
thus:
y=4 
next
multiply the top equation by 6 and the bottom equation by 7 then subtract the bottom from the top equation gives us:
-2x=-6
hence;
x=3
therefore:
Total time taken to do 1 sum is x=3 nanoseconds
Total time taken to do 1 product is y=4 nanoseconds