Question

What is the solution of the sollowing system of equations?
3x+2y+z=7
5x+5y+4z=3
3x+2y+3z=1

Answer 1

would i multiply the first equation by -1 and then add that and the third?
-3x-2y-x=-7
3x+2y+3z=1
?

Answer 2

Yes. That would get rid of the x variable using equations 1 and 3.
Eliminate the x variable again but this time using equations 1 and 2. Multiply the first equation by 5 and the second equation by -3 and add them to get rid of x.
You will now have two equations and two unknowns y and z. Eliminate one of the variables and solve.

Answer 3

yeah do it..

Answer 4

but that would eliminate the x and the y?

Answer 5

True which makes life a lot easier! You can straightaway solve for z!

Answer 6

3x+2y+z=7 (1)
5x+5y+4z=3 (2)
3x+2y+3z=1 (3)

Multiply (1) by -1 and add to (3):
-3x-2y-z=-7
3x+2y+3z=1
add
2z = -6
z = -3
Put z = -3 in (1) and (2) and solve for x and y.

Answer 7

im a little confused, i put z into either of the equations to solve for x and the for y?

Answer 8

Put z = -3 in (1):
3x+2y+(-3)=7
3x+2y=10 (4)

Put z = -3 in (2):
5x+5y+4(-3)=3
5x+5y-12=3
5x+5y=15
x + y = 3 (5)

Use equations (4) and (5) to solve for x and y. It is two simultaneous equations and two unknowns.

Answer 9

that just confused me more,

Answer 10

We started with three equations and three unknowns.
Then we reduce it to two equations and two unknowns:

3x+2y=10 (4)
x + y = 3 (5)
multiply equation (5) by -2 and add it to equation (4):
3x+2y=10
-2x-2y=-6
add
x = 4
Put it in (5) and solve for y:
4+y=3
y = -1

x = 4, y = -1, z = -3.