Simultaneous Equations
5 minQuiz at the end
What are Simultaneous Equations?
Simultaneous equations are two (or more) equations that are both true at the same time. The solution is the pair of values (x, y) that satisfy both equations.
Method 1: Elimination
Add or subtract equations to eliminate one variable:
x + y = 7 β¦β x - y = 3 β¦β‘
β + β‘: 2x = 10 β x = 5 Substitute into β : 5 + y = 7 β y = 2
Solution: x = 5, y = 2 β
Method 2: Substitution
Rearrange one equation and substitute into the other:
y = 2x β¦β x + y = 9 β¦β‘
Substitute β intoβ‘: x + 2x = 9 β 3x = 9 β x = 3 From β : y = 2(3) = 6
Solution: x = 3, y = 6 β
Method 3: Graphical
Plot both lines on the same axes. The intersection point is the solution.
Number of Solutions
| Situation | Solutions |
|---|---|
| Lines cross | One unique solution |
| Lines are parallel (same gradient, different intercept) | No solution |
| Lines are identical | Infinitely many solutions |