solve the given system of equations?

Question

x-y-z=1
-x+2y-2z=-3
5x-3y-11z=1

x=
y=
z=

Answer 1

Use determinants,( I know this sum very well)

Δ = | 1 -1 -1|
... ...| -1 2 -2|
... ...| 5 -3-11|
=1(-22 - 6) + 1(11+10) - 1(3-10) = -28+21+7 = 0!!

Δ(1) = | 1 -1 -1|
....... ...| -3 2 -2|
...... ....| 1 -3-11|
= 1(-28)+1(33+2)-1(9-2) = 0

Δ(2) = | 1 1 -1|
...... ....| -1 -3 -2|
...... ....| 5 1-11|
=(33+2)-(11+10)-(-1+15)=0

Δ(3) = | 1 -1 1|
....... ...| -1 2 -3|
....... ...| 5 -3 1|
=(2-9)+(-1+15)+(3-10)=0

We see that,Δ=Δ(1)=Δ(2)=Δ(3) = 0
Hence by Cramer's method, we may conclude that the system of equation have infinite number of solutions.

Answer 2

Add the first two rows together. That eliminates x.
Now multiply the (original) second row by 5 and add it to the third row. That also eliminates x.

You now have two equations with two variables. Multiply one if needed to make a second variable get eliminated. You will find that in fact both variables get eliminated, and you end up with 0 = 0.

That means there is no unique answer to this system. Need more help? Send an IM or look below for a more complete answer.

Answer 3

The simplest way of solving this equation is to use determinants.
Equation above is already written correctly with constants at one side. each determinant will have size 3X3. If D stands for determinant and RHS indicates right hand side.
x / D( RHS constant, coefficient of y,coefficient of y) of 3 rows, one each for one equation
= (or equals)
y / D (coefficient of x, RHS constant, coefficient of z)
= (or equals)
z/ D (coefficient of x , coefficient of y ,RHS constant,)
= (or equals)
1/D (coefficient of x , coefficient of y, coefficient of z)
solving the equations we get x=0, y= - 5/4 (minus 5/4), z=1/4
in the above question the moment we find the first determinant we get x = 0 and then we can find y & z by substitution.
As I am not well versed with computers in creating the determinants - I cannot explain better - sorry .

Subhash

Answer 4

look on the 1st equation. in case you knew what x grow to be you will possibly be able to desire to unravel it, right? yet you do comprehend what x is. the 2nd equation inform you. So, rewrite the 1st equation as 2(4y+3) +8y = 6. Then resolve for y via multiplying via and mixing like words.

Answer 5

You can use substitution or elimination twice, or you can put the equations into a matrix. You can solve matrices on your graphing calculator or by hand.

Answer 6

x=3
y=1
z=1