What is the solution to the following system of equations
-2x+3y+z=5
x+5y+2z=17
To do this, I used elementary operations and isolated x to get 13y+5z=37. Is that correct so far? How would I continue?
with 3 unknowns and only two equations, there will be no unique solution.
It should be
13y+5z = 39
so, pick any y and z that fit, and then figure x.
Or, you can evaluate y and z in terms of x:
y = 5x-7
z = 13(2-x)
Now you can pick any value for x, and then figure y and z.
In 3D, you have the intersection of two planes, which will be a line, not just a single point.