Solve systems of linear equations by adding or subtracting equations (with scaling when needed) to eliminate a variable.
Substitution is not the only way to solve a system. Elimination works directly on the two equations themselves: since both sides of an equation are equal, you may add the left sides together and the right sides together, and the result is still true. If one variable has opposite coefficients in the two equations (like +4y and -4y), adding makes it vanish completely - eliminated - leaving one equation in one variable, which you already know how to solve.
Often the coefficients do not line up on their own. The fix is to multiply one or both equations by a constant first - this does not change what the equation means, only how it is written (just like multiplying both sides of x = 3 by 2 still means x = 3). Once a pair of matching or opposite coefficients exists, add or subtract to eliminate, solve for the survivor, then substitute back into either original equation to find the other variable. Always check both original equations at the end.
Mastery looks like: They can look at a pair of equations, decide what to multiply (if anything), eliminate cleanly, and check the answer in both originals.
Common stumbles: Multiplying only one side of an equation instead of every term; adding when they should have subtracted (or the reverse), which flips a sign silently.