Show that the system of equation $\displaystyle

x - 3y -8z = -10;

$$\displaystyle

3x+y-4z=0;

$ and $\displaystyle

2x+5y+6z =13

$ is consistent and find the solution .

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- May 3rd 2009, 10:24 PMzorroShow that the system of equation is consistent
Show that the system of equation $\displaystyle

x - 3y -8z = -10;

$$\displaystyle

3x+y-4z=0;

$ and $\displaystyle

2x+5y+6z =13

$ is consistent and find the solution . - May 4th 2009, 12:30 AMmr fantastic
- Dec 14th 2009, 01:39 PMzorroI am still not getting the anw=swer
- Dec 14th 2009, 05:36 PMmr fantastic
OK, the determinamt

**is**equal to zero (I should have checked). This means that either there's no solution or an infinite number of solutions. So my suggestion is no good after all.

In fact, since x = 3y + 8z from the first equation, the second and third equations become:

y + 2z = 0 and y + 2z = 13/2.

Therefore the equations are**IN**consistent and there is no solution to be found. - Dec 19th 2009, 08:36 PMzorroDo u have a links for this
- Dec 19th 2009, 11:02 PMCaptainBlack
- Dec 19th 2009, 11:54 PMmathaddict
HI

$\displaystyle x-3y-8z=-10$ ---- 1

$\displaystyle 3x+y-4z=0$ -----2

$\displaystyle 2x+5y+6z=13$ ---- 3

1x2 -3 $\displaystyle y+2z=3\Rightarrow z=\frac{3-y}{2}$ ---4

Substitute 4 into equation 3 .

$\displaystyle 2x+5y+6(\frac{3-y}{2})=13$

$\displaystyle x=2-y$

so (x,y,z)=(2-y , y , (3-y)/2)

(x,y,z)=y(-1,1,-1/2)+(2,0,3/2) where $\displaystyle y\in R$

and if y=1 , (x,y,z)=(1,1,1) which agrees with CB .

Not sure if this is right though . - Dec 20th 2009, 01:02 AMzorroI couldnt understand
- Dec 20th 2009, 01:42 AMdedust
- Dec 20th 2009, 01:45 AMCaptainBlack
- Dec 20th 2009, 02:58 AMmr fantastic
- Dec 27th 2009, 01:09 AMzorro
sorry, but i am still unable to understand this ????????????

- Dec 27th 2009, 01:44 AM11rdc11
I'm not sure if this is a right approach to this problem due to teaching myself the material but could you not just use gauss-jordan elimination.

The last row would be

$\displaystyle 0x +0y + 0z = 0$

therefore showing that there is infinite number of solutions