Question

X+y+z=3 x-y+z=2 x+y-z=1

Answer 1

Answer:

Step-by-step explanation:

I'm assuming you are solving this system for x, y, and z.  Do it this way:

Combine the first 2 equations and the second 2 equations and eliminate the y's.  The first 2 equations:

x + y + z = 3

x - y + z = 2

which solves to

2x + 2z = 5

The second 2 equations:

x - y + z = 2

x + y - z = 1

which solves to

2x = 3 so

x = 3/2 or 1.5

Now sub that x value into the bold equation above to get:

2(1.5) + 2z = 5 and

3 + 2z = 5 and

2z = 2 so

z = 1

Now we plug back in to solve for y:

1.5 + y + 1 = 3 and

2.5 + y = 3 so

y = .5

The solution set then is (1.5, .5, 1) or in fraction form:

$(\frac{3}{2},\frac{1}{2},1)$