1.

x + y = 1 + z

z = x + y - 1

2.

x - y + (x + y - 1) = 3

2x - 1 = 3

x = 2

3.

x - y - z = -5

y = x - z + 5

y = x + 5 - x - y + 1

2y = 6

y = 3

4.

z = x + y - 1

z = 2 + 3 - 1

z = 4

Check Method:

2 + 3 - 4 = 1

2 - 3 + 4 = 3

2 - 3 - 4 = -5

This is quite an easy system, since it is possible to eliminate more than one variable at the same time.

Adding the first two equations eliminates both y and z, giving 2x=4 and then x=2.

Subtracting the third equation from the second equation eliminates both x and y, giving 2z=8 and then z=4.

Substituting x=2 and z=4 into any one of the equations (say the first equation) gives 2+y-4=1 and then y=3.

So the solution is x=2, y=3, and z=4.

Check: We verify that the solution makes each equation true.

2+3-4 = 5-4 = 1

2-3+4 = -1+4 = 3

2-3-4 = -1-4 = -5.

The solution works!

Have a blessed, wonderful day!

What are we supposed to do? Are we supposed to find all of them or just one variable? Are we supposed to use substitution or elimination?