You can start by choosing the value of one of the variables, and then find the others.
Example Solution:
x+y+z = 7 y+z = 6 z = 2
Practice makes perfect
Since we want our system to have one solution, we can start by choosing one of the variables values to construct the solution of the system. Let's have a look at our system of equations.
x+y+z = 7 & (I) y+z = & (II) z = & (III)
We can start by choosing a value for x — for instance, x=1. Then we can substitute this value in Equation (I) and simplify to find the value we can use on the right-hand side of Equation (II).
Now we know that y+z should be 6 for mathematical consistency. We can choose any value we want for y. Let's try y=4. Then, we can substitute this in Equation (II) and find the value for z.
We have constructed a system of equations with the solution x =1, y=4, and z=2.
x+y+z = 7 y+z = 6 z = 2
Notice that we could have chosen any value for x at the beginning, or started by choosing the value for z and work from Equation (III) to (I). There are infinitely many possible solutions satisfying the requirements of this exercise, and this is only an example solution.
