The sum of three numbers is 34. The third number is 4 less than the sum of the first two numbers. The second number is 1 larger than the first. Find the numbers

Question

system of linear equation problem I do not know how to solve.

Answer 1

If x, y, and z are those three number, then

x+y+z=34

x+y=z+4

x+1=y

 

If you solve this system of equations you find the numbers: 

x=9, y=10, z=15.

 

It is easy to solve:

The first equation minus  the second one gives 2z=30, z=15

Then from the second and third equations:

x+y=19
x-y=-1

 

2x=18

x=9

y=10