[Solved] 3x4 system of equations 1. The problem statement, all variables and given/known data Consider the following system of three equations in x, y and z. 2x + 4y + 5z = 17 4x + ay + 3z = b 8x + 7y + 13z = 40 Give values for a and b in the second equation that make this system consistent, but with an infinite set of solutions. 3. The attempt at a solution I found the answers a= -1, b=6 easily enough. I was told by my teacher that if a system of three equations has infinite solutions, one of the equations can be found from the other two. I multiplied equation 1 by 2 and subtracted the result from equation 3. This gave: 4x - y + 3z = 6 and so finding the values of a and b was pretty simple from there. Plugging the numbers into a calculator gave an infinite number of solutions. My question is, how can I better explain how to get a and b from the provided data? My method just seems like an educated guess rather than solid evidence - I don't think it'd look very good to an examiner. Cheers.