# Solve the system of equations

• Jun 9th 2013, 02:51 PM
Mc3
Solve the system of equations
How do you solve this system?
9x+ 9y + 7z = 6
-45x + 18y + 21z = -12
thanks!!
• Jun 9th 2013, 03:22 PM
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.
• Jun 9th 2013, 03:57 PM
Mc3
Re: Solve the system of equations
Yeah that's what I thought so too and I am so confused my teacher assigned us this.
• Jun 9th 2013, 05:19 PM
jpritch422
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.
• Jun 9th 2013, 09:48 PM
ibdutt
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