I need help solving these simultaneous linear eguations?

Question

x-2y+z=-5
2x-y+z=1
2x+y+2z=10



x+2y-z=-3
2x+y+z=6
-2x+2y+2z=3

Answer 1

Using matices to do this

[ 1 -2 1] * [x] = [-5]
[ 2 -1 1] [y] [ 1]
[2 1 2] [z] [10]

AX = B
A*A^(-1)X = A^(-1)B
X = A^(-1)B

SO we need the inverse of A this can be worked out using a long and tedious method or just use a calculator

A^-1 = [ -.6 1 -.2]
[ -.4 0 2]
[.8 -1 .6]

A^-1B = [2}
[4}
[1]
so x =2 y=4 z=1

now you do the other one
Check
2 - (4*2) +1 = 2 - 8 +1 = -5

Answer 2

Eliminate one unknown from each equation at a time.
x - 2y +z = 5 Multiply both sides of the equation by 2
2x - 4y + 2z = 10 Now take one of the other equations
2x + y + 2z = 10 Subtract leaving -5y = 0 i.e. y = 0
Use another equation 2x - y + z = 1
2x - 4y +2z = 10 Subtract
3y - z = -9, Substitute 0 for y and z = 9 Substitute these into
x - 2y + z = 5, i.e. x - 0 + 9 = 5 hence x = -4
Proof:- 2x - y + z =1 i.e. -8 - 0 + 9 = 1

Do the next one yourself :- x = y = z = 1.5

Answer 3

Mulitply the first by -2 and add to the second:

-2x + 4y - 2z = 10
2x -y + z = 1
------------------------
3y - z = 11
z = 3y - 11

Do the same thing with 1 & 3:

-2x + 4y - 2z = 10
2x + y + 2z = 10
5y = 20
y = 4

Substitute this back in the previous equation:

z = 12 - 11 = 1

Then you can get x:

x - 8 + 1 = -5
x - 7 = -5
x = 2

Now, do the same thing for the second set. :-)

Answer 4

For substitution, you resolve for on variable in terms of the different one, and plug that into the 2nd equation. for occasion: a million) 2x-5y=6 => 5y=2x-6 => y=(2x-6)/5, then plug in this "y" to the 2nd equation in this undertaking.. 3x + 4((2x-6)/5) = 32... 3x + (8x-24)/5 = 32 15x/5 + (8x-24)/5 = 32 15x + 8x - 24 = 32(5) = a hundred and sixty 23x = 184, or x = 8.. Then plug that x into the two equation to unravel for "y" 2(8) - 5y = 6 sixteen - 5y = 6 5y = sixteen - 6 = 10, so y = 2 comparable for #2

Answer 5

1) x= -4 y=0 z= 9

Sorry, that's all I know. I'm only in 6th grade after all.

Answer 6

yep. a 3x3 Matrix.

Answer 7

set up a matrix and solve it with a calculator.

Answer 8

Get x in terms of y&z. Get y in terms of z. Get z
Substitute and get the value y and x