Question

3x+2y+4z=12

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
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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