Show that this equation is NOT consipten [ 2 x+6 y+11=0 6 x+20 y-6 z-3=0 6 y-18 z+1=0 ]

Question

Show that this equation is NOT consipten [ 2 x+6 y+11=0 6 x+20 y-6 z-3=0 6 y-18 z+1=0 ]

Answer 1

To determine if the given system of equations is consistent, we need to check if there exists a set of values for

,

, and

that satisfies all three equations simultaneously. If such a set exists, the system is consistent; otherwise, it is not.Let's analyze each equation:1.

2.

3.

First, let's solve the third equation for

:

Now, substitute

into the second equation:

Now, we have two equations with two variables (

and

):1.

2.

Let's solve these two equations simultaneously. We can use the elimination method. Multiply the first equation by 3:

Now, subtract the second equation from this result:

This is a contradiction, which means there is no set of values for

,

, and

that satisfies all three equations simultaneously. Therefore, the given system of equations is not consistent.

Question

Show that this equation is NOT consipten [ 2 x+6 y+11=0 6 x+20 y-6 z-3=0 6 y-18 z+1=0 ]

Solution

Resposta