 # Determine whether the given (2 times 3) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two Tyra 2021-02-03 Answered
Determine whether the given system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line, that is, give equations of the form

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Step 1
The given system of linear equations

We need to determine whether the given system of linear equations represents coicident planes, two parallel planes, or two planes whose intersection is a line.
Let be normal vectors of both the equations.
Then are not parallel.
Let in the system of linear equations
(1)
(2)
(1)
Replace in the second equation

Replace , then

Hence, the plane intersect in a line and the parametric equations are