Solving Systems of Linear Equations
The Elimination Method (Addition Method)
Also known as способ сложения — often the fastest way to solve a system!
📋 Review: Methods We Know
So far, you've learned two methods for solving systems of linear equations:
📈 Graphical Method
Graph both lines and find the intersection point. Visual but can be imprecise.
🔄 Substitution Method
Solve one equation for a variable, then substitute into the other.
➕ Elimination Method
NEW! Add or subtract equations to eliminate a variable. Often the fastest!
💡 The Key Idea
The elimination method works by adding or subtracting entire equations to make one variable disappear.
This leaves you with a single equation in one variable — which you already know how to solve!
Why Does This Work?
If equals are added to equals, the result is equal:
If $a = b$ and $c = d$
Then $a + c = b + d$ ✓
Adding entire equations preserves equality because each side of each equation represents the same value.