# Determine whether the given (2 times 3) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two

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