# How to find symmetric equations for the line of intersection of two planes?

Hi, I have been at this single problem for two hours with nothing to show for it.

Find symmetric equations for the line of intersection of the planes.
z = 3x - y - 7
z = 4x + 2y - 6

They also give me one of the symmetric equations, z/10.

I have over 3 pages of work for this. I tried moving the z over and using the cross product, and then setting y equal to 0 to find x and y and then using that to find a point on the line of intersection. I then get an equation for a line, but its wrong. I don't know what else to do.

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nevermind i solved it

This is asking for symmetric equations of lines, that is to say, of the form:

$$\frac{x-x_0}{a} = \frac{y - y_0}{b} = \frac{z - z_0}{c}$$

right? Are you doing this? They tell you one of the forms:

$$\frac{z - z_0}{c} \rightarrow \frac{z}{10}$$

When you say that you find an equation of a line that is "wrong" does that mean you have checked it out and it is not agreeing with something, or do you have the final answer? If you are not making steps towards obtaining a form such as that listed above, your result may appear wrong because you are comparing different forms of a final result.

Taking cross products does not make sense in the regard of scalar equations, there are no vectors here unless you construct them. Please advise.

Edit: ok