Math basics › Lines and systems
Systems of equations
What a solution is
The point where the two lines cross — the (x, y) that satisfies both at once.
Substitution
Get one variable alone in one equation, put that expression into the other. Best when something is already alone, or nearly.
Elimination
Add or subtract the equations so one variable cancels. Multiply one equation first if you need to make the coefficients match.
No solution, or infinitely many
Parallel lines never meet, so there is no solution. Identical lines meet everywhere. If your algebra ends in 0 = 5 it is the first; if it ends in 0 = 0 it is the second.