# Problem description

Having system of equations as input (in whatever format):

``````x + y = 6
2x + y = 9
``````

I would like to output manual, step-by-step high-school-like solution. In other words applying rules from a ruleset one at a time:

``````Step 1:
x = 6 - y
2x + y = 9
Step 2:
x = 6 - y
2 * (6 - y) + y = 9
Step 3:
x = 6 - y
12 - 2y + y = 9
Step 4:
x = 6 - y
-2y + y = 9 - 12
Step 5:
x = 6 - y
-y = 9 - 12
Step 6:
x = 6 - y
-y = -3
Step 7:
x = 6 - y
y = 3
Step 8:
x = 6 - 3
y = 3
Step 9:
x = 3
y = 3
``````

Let's assume that system is always solvable. I'm trying to write this program in Node, but underlying technology is a secondary issue.

# Question

Is there some terms rewriting system / expert system which can do this? Or is this problem more complex then I think and there is no simple, automated solution?

• Only simple linear equations like the one in this example? Or different types? Feb 26, 2020 at 21:59
• Only simple equations like above + parenthesis and integer powers. The most complicated ones should look like this: (x - 2)^2 + x^4 = 17 + y Mar 2, 2020 at 12:08
• For linear equations - like the one in your question - one could use the standard Gaussian elimination. For polynomial equations, however, like the one in your comment, there may not even be a solution, or it may only be possible to find a symbolic, closed solution, only a numerical one. I would recommend to google for "polynomial equation solver". What you are asking for might be part of some computer algebra systems, check this list on Wikipedia Mar 2, 2020 at 12:22