Question

Systems of Equations in three variables

Determine whether (-3, -1, 4) is a solution of the system

2x-2y-3z=-16
4x-3y+3z= 3
x+ y - 5z = -24

I'm having troubles with this problem could someone explain this problem to me. Also this next problem as well please...

solve the system.

x+ y+ z = 7
x- y= 2z = 4
2x+ y + z = 5

Answer 1

thank you @JamesWolf

Answer 2

well, as far as determining if a point is a solution. Whack it into every equation and see if they hold

to solve the system, you need to get an equation for just one of the variables. Theres loads of ways you could do this, what i would do is add equation 1 and 2 to get

x + y + z + x - y + 2z = 7 + 4

2x + 2z = 11

then I would take away 2x the top row from this

2x + 2z - 2x -2y -2z = 11 -7

2y = 4
y = 2.

now you have a way in. you can replace this value of y into any of the equations and solve for x or z. replace that into "2x + 2z = 11" to solve for an other variable.

and so on like this until you get all the variables.

generally hteres no quick way to do it, and its a matter of doing a few to spot which moves will solve it quickest

Answer 3

im presuming the second line was not

x- y= 2z = 4

but

x - y + 2z = 4

?

Answer 4

well thats wrong somewhere lol.

http://math.bd.psu.edu/~jpp4/finitemath/3x3solver.html

using that to check the answer

Answer 5

yes the = was suppose to be a +

Answer 6

http://symbolab.com/solver/system-of-equations-calculator/x%2By%2Bz%3D7%2C%20x-%20y%2B2z%20%3D%204%2C2x%2B%20y%20%2B%20z%20%3D%205%20/?origin=button

Answer 7

that solves them and gives you steps

Answer 8

click the little + by the show steps, to see either elimination method or substitution

Answer 9

Thank you!!! This helps a lot thank you yea the fact that it will show its steps helps because I am a very visual person.

Answer 10

Yeah me too. Nice that it gives you both elimination or substitution method

Answer 11

Yes definitely do you have any more math sites? That you have that help you?