3. Which equation is equivalent to [tex] x + 3y- z = 3 [/tex]
Now multiply both the sides by 4 we get
[tex] 4*(x + 3y- z = 3)\\\\\Rightarrow4*(x+3y-z)=4*3\\\\\Rightarrow4x+12y-4z=12\\\\\ \text{Hence the equivalent equation is } 4x+12y-4z=12\\ [/tex]
4.
We need to find the point which satisfies the given equation
[tex] 3x-2y + 4z =-12\\\\\text{Substitute the point (2,-2,3) we get}\\\\3*2-2(-2)+4(3)=6+4+12=22\not\equiv -12\\\\\text{Hence this point does not satisfy}\\\\\text{Now check with the point (4,16,2)}\\\\3*4-2*16+4*2=12-32+8=12=True\\\ \text{Hence the required point is} (4,16,2)\\ [/tex]
