Linear Equations

Core approach:

ax + b = c => x = (c - b) / a
For two equations, eliminate one variable or substitute.

Speed rules:

Convert word statements to equations immediately.
If options exist, substitute options.
For age problems, use current age as variable; age difference stays constant.
For digits problems, two-digit number with tens digit x and units digit y is 10x + y.

Common equation patterns:

Sum known: x + y = S
Difference known: x - y = D
Ratio known: x/y = a/b => x = ak, y = bk

Linear Equations​