How do i solve inequalitites with three variables. I still can't figure it outplease help.
x+y=1
y-z=-3
2x+3y+z=1
THE ANSWERS ARE3,-2,1 HOW DID THEY GET THAT ANSWER.
This can be solved a number of ways.
1) subsitition
2) determinants
3) matricies.
Substution:
x= 1-y
y= z+3 or x= 1-z-3
In the third equation , put those two things for x, and y.
2x+3y+z=1
then solve for z. Then go back and solve for x and y.
I've done that already such as
the book states the following
that the answer is -x-y=-1
how did they get there after adding equation 2 and three
Substitute x = 1-y and z = y+3 in the third equation. Then you get an equation in y only:
2(1-y) + 3y + (y+3) = 1
2y + 5 = 1
y = -2
Then use the equations for x and z again.
x = 1-(-2) = 3 etc.
To get the answer -x-y=-1, you need to add equation 2 and equation 3 after substituting x = 1-y and z = y+3. Let's break it down step by step:
Equation 2: y - z = -3
Equation 3: 2x + 3y + z = 1
Substitute x = 1-y in equation 3:
2(1-y) + 3y + z = 1
Now, simplify:
2-2y + 3y + z = 1
-z + y + 2 = 1
y - z = -1
So, after adding equation 2 (y - z = -3) and equation 3 (y - z = -1), you get -x - y = -1.
It seems like there might be a mistake in your explanation of the book's answer. The correct equation after adding equation 2 and equation 3 should be -x - y = -1, not -x - y = -1.