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 ARE X=3,Y=-2,Z=1
i KNOW THE ANSWERS I JUST DON'T KNOW HOW THE BOOK GOT THE ANSWERS . i 'VE TRIED MANY DIFFERENT WAYS AND I STILL DONT' UNDERSTAND IT PLEASE EXPLAIN IT.
i KNOW THAT I HAVE TO ADD EQUATION 2 AND THREE TO GET THE FOLLOWING
2X+3Y+Z=1
Y-Z=-3
IN ORDER TO GET
2X+4Y=-2
THEN I DON'T KNOW FROM HERE
There a couple ways to solve this. You have
x+y = 1
y-z =-3
2x+3y+z= 1
You could first show
x=1-y and z=y+3 and substitute them into the 3rd equation to get
2(1-y)+3y+y+3=1 and solve for y to get
2-2y+3y+y+3=1
5+2y=1 so 2y=-4 and y=-2
then put this into the first two equations to solve for x and z.
Let's start by substituting y = -2 into the first equation, x + y = 1:
x + (-2) = 1
x - 2 = 1
Now, add 2 to both sides of the equation:
x = 1 + 2
x = 3
We have x = 3 and y = -2. Now let's substitute these values into the second equation, y - z = -3:
-2 - z = -3
Add 2 to both sides of the equation:
z = -2 + 3
z = 1
So, we have x = 3, y = -2, and z = 1 as the solution to the system of equations.
To summarize the steps we took:
1. Substituted y = -2 into the first equation.
2. Solved for x.
3. Substituted x = 3 into the second equation.
4. Solved for z.
I hope this helps in understanding how to solve inequalities with three variables.