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I don't understand how to prove this algebraically. I don't even have an idea how to show that two planes never intersect a line using the following definitios they ask you to use.

Explain algebraically why two planes can never intersect in only a point. You must use the words : linear system, augmented matrix, RREF, leading ones.

The equation of each of the planes involves three variables.

If one of these variables is solved for in terms of the other two,

this can then be inserted into the other equation.

Suppose the two planes are f(x,y,z) and g(x,y,z).

Take f(x,y,z) and solve for z in terms of x and y.

Put this equation for z into g, and then we have g in terms of x and y only.

It is known that if there is an equation that only has two variables, it is a line.

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