What is the x-value of the solution to the system?

Question

x-y+3z=-1

5x+z=0

x+4y+z=4

Answer 1

5x+z=0

 

=> z= -5x

 

now, x-y+3z=-1

 

       => x-y+3(-5x)= -1

        

        => x-y-15x = -1

 

         => -y-14x = -1

 

          => y= 1-14x

 

Now if we put y and z value in the third equation we get-

 

  x+4y+z=4

  

 => x+4(1-14x)+(-5x)=4

 

 => x+4-56x-5x=4

 

 => 4-60x=4

 

 => 60x = 4-4

 

 => 60x=0

 

 => x = 0

 

Then, y = 1-14x

 

        => y= 1- 14*0

 

         => y= 1

 

and z= -5x

 

      => z= -5*0

 

       => z= 0

 

You can proof that the answer is right by putting the values of x, y, and z in any of these equation.