# Thread: Solve the system of equations

1. ## Solve the system of equations

How do you solve this system?
9x+ 9y + 7z = 6
-45x + 18y + 21z = -12
thanks!!

2. ## Re: Solve the system of equations

It is impossible to solve a system of equations with three variables with only two equations. you need three. Otherwise there are multiple solutions that could work.

3. ## Re: Solve the system of equations

Yeah that's what I thought so too and I am so confused my teacher assigned us this.

4. ## Re: Solve the system of equations

You can look at the two equations as the equations of two planes. The intersection of those two planes form a line in 3D space. The solution(s) to the two equations would be any point on that line, but you would first have to find the equation of the line. That is the only way I know of finding values of x, y and z. There could be an infinite number of solutions, but each point (x,y,z) must fall on that line.

5. ## Re: Solve the system of equations

If we have two planes with equations P1=0 and P2= 0 then the equation of the line of intersection would be P1 + k P2= 0 In this case
(9x+ 9y + 7z - 6) + k ( -45x + 18y + 21z +12) = 0