Question

3x+2y+4z=12

X+y+2z=6
(X=0,y=4,z=1)
Determine if the given 2 lines intersect at the given point. Explain your reasoning.
-2x-4y+z=8
4x+2y=-5
(x=-2,y=0,z=3) same as up above

Answer 1

Substitute the given points into each equation and if the answer is as intended for both equation, then it means the given points are the intersection point

Given points x = 0, y = 4, and z = 1
Equation 1:
3x + 2y + 4z = 3(0) + 2(4) + 4(1) = 0 + 8 + 4 = 12
Equation 2:
x + y + 2z = 0 + 4 + 2(1) = 6

Both equation 1 and equation 2 give the intended answer; 12 and 6 respectively, hence the given point is the intersection point
---------------------------------------------------------------------------------------------------------------

Given point : x = -2, y = 0, and z = 3

Equation 1:
-2x - 4y + z = -2(-2) - 4(0) + 3 = 4 - 0 + 3 = 7
Equation 2:
4x + 2y = 4(-2) + 2(0) = -8

The answers are not as intended, hence the given point is not the intersection point