Thread: How to solve a system of linear equations when there are less rows than variables?

I took a year off from Math before deciding to major in it, so I'm a little rusty.

I've come to a point in a problem where I have 2 linear equations:

-2a+3b+9c=0
and
-2a+5b+4c=0

I'm unsure of how to solve these 2 equations. I can cancel out one of the variables, but after than, I don't know how to eliminate the next one so I can isolate the value of the 3rd variable. The Cramster expert answer says a = -33, b=-10, and c = -4.

Any help is greatly appreciated.

P.S. I know this looks like a linear algebra question, but this problem came from my multivariable calculus HW where those equations are the equation of the line orthogonal to a plane and the equation of the point on that plane.

Peter, subtract the two equations to get:



Then, all points along this line will satisfy the system. Select .

Which gives us:

Then, plug these two results into our first equation, to get:



To give us a final result of .

This is not the only correct answer for this system. Hope this helps, thanks!

Originally Posted by Dark Sun

Peter, subtract the two equations to get:



Then, all points along this line will satisfy the system. Select .

Which gives us:

Then, plug these two results into our first equation, to get:



To give us a final result of .

This is not the only correct answer for this system. Hope this helps, thanks!

Sorry, but I'm confused as to how you came up with c = -4. Why or how did you come to select -4 as the value of c?

There are more than one solution. You could also select .

I selected -4 so that the answer would agree with the solution that you had already known.

Any point along the line would return a valid solution.

Do you understand now?

Yup, thanks a lot man.