Linear equations are the foundation of algebra, calculus and most of finance. Three solving methods cover almost every situation.
If you have ever stared at a number on a form and wondered where it came from, you are not alone. Linear equations are the foundation of algebra, calculus and most of finance. Three solving methods cover almost every situation.
Solve one variable, plug into the other. Best for systems where one equation is already isolated.
Add or subtract equations to cancel a variable. Best for systems with matching coefficients.
Express as Ax = b, solve via inverse or row reduction. Best for systems with many variables.
Plot both lines, find intersection. Visual, intuitive, good for two-variable systems.
What's the difference between linear and non-linear? Linear has variables to first power only. y = 2x + 3 is linear; y = x² + 1 is not.
Are systems of equations harder? More variables, same logic. Three methods scale up well.
Run your own numbers before you trust a rule of thumb. Two minutes saves a lot of regret.