Solve the following system: x + y+ z = 4?

Question

x + y + z = 4
x -2y - z = 1
2x -y -2z = -1

Please show me how each step is done??

CRAMERS METHOD PLEASE.

Answer 1

x+y+z=4
x-2y-z=1
2x-y-2z=-1

Answer 2

a million) x + y = 4 2) x + z = 4 3) y + z = 4 From equation a million: x + y = 4 x = 4 - y replace for x in equation 2: x + z = 4 (4 - y) + z = 4 z - y + 4 = 4 z = 4 - 4 + y z = y replace for z in equation 3: y + z = 4 y + y = 4 2y = 4 y = 4/2 y = 2 z = y, so z = 2 replace to discover x: x + y = 4 x + 2 = 4 x = 4 - 2 x = 2 x = 2, y = 2, z = 2

Answer 3

From the first eqn.
Step 1: z=4-(x+y)
Step 2:put this value of zin the other two eqns.
Step 3:then you will get a system of simultaneous eqn. in x and y.
Step 4:Then solve for x and y
Step 5: Put the values of x and y thus obtained in z=4-(x+y) to get the value of z.

Answer 4

I see crammer's now... Did you add it later? Since I can't put brackets nicely, I just put them in rows

x+y+z=4
x-2y-z=1
2x-y-2z=-1

For the coeeficient matrix M

1 1 1
1 -2 -1
2 -1 -2

Find the Determinant of the above and call it |M|

To calculate the determinant, easy way is to extend the matrix by adding the first two columns. Multiply and add complete diagonals from left to right and call it S1. Multiply and add complete diagonals from right to left and call it S2. Substract S2 from S1.

Say the matrix is

a11 a12 a13 a11 a12
a21 a22 a23 a21 a22
a31 a32 a33 a31 a32

S1=(a11*a22*a33)+(a12*a23*a31)+(a13*a21*a32)
S2=(A12*a21*a33)+(a11*a23*a32)+(a13*a22*a31)

Using the above you get the determinant of our matrix |M| = 6

Now form another matrix by replacing the 'x' column with the result comumn (on the right side of the = sign) which is

4 1 1
1 -2 -1
-1 -1 -2

Form the extended matrix and determine it's determinant and call it |Mx|

4 1 1 4 1
1 -2 -1 1 -2
-1 -1 -2 -1 -1

If you use the above formula (a11, a22 etc.,), you will get the determinant

|Mx| = 12

Value of x is Mx/M = 12 / 6 = 2

Find the values of y and z using the similar way

Answer 5

hey tiff plz chat with me i like u dear , hey man thats funny coz tell me in which method u want it to be solved ???
Cramers method , guass-jorden or in the Matrices method ???

Answer 6

I don't know Cramer's method... that's with the brackets and stuff, right... oh well... sorry to waste your time... no 10 points for me...