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MASTER SIMULTANEOUS EQUATIONS IN ALGEBRA!
SIMULTANEOUS EQUATIONS ARE ONE OF THE MOST IMPORTANT TOPICS IN MATHEMATICS, USED IN ALGEBRA, GEOMETRY, OLYMPIADS, AND UNIVERSITY ENTRANCE EXAMS.

👉 A SIMULTANEOUS EQUATION IS A SET OF TWO OR MORE EQUATIONS WITH TWO OR MORE VARIABLES THAT MUST BE SOLVED TOGETHER.
THE SOLUTION IS THE VALUE OF THE VARIABLES THAT SATISFY ALL EQUATIONS AT THE SAME TIME.

✍️ COMMON METHODS TO SOLVE SIMULTANEOUS EQUATIONS:

SUBSTITUTION METHOD

FROM ONE EQUATION, EXPRESS A VARIABLE IN TERMS OF THE OTHER

SUBSTITUTE INTO THE SECOND EQUATION

SOLVE STEP-BY-STEP

📘 EXAMPLE:
x + y = 10
2x – y = 4
SOLUTION: x = 14/3, y = 16/3

ELIMINATION METHOD

ADD OR SUBTRACT EQUATIONS TO ELIMINATE ONE VARIABLE

SOLVE THE RESULTING EQUATION

SUBSTITUTE BACK TO FIND THE OTHER VARIABLE

📘 EXAMPLE:
3x + 2y = 12
2x – 2y = 4
SOLUTION: x = 2, y = 3

GRAPHICAL METHOD

PLOT BOTH EQUATIONS ON A GRAPH

THE INTERSECTION POINT IS THE SOLUTION

MATRIX METHOD (CRAMER’S RULE)

USE DETERMINANTS TO SOLVE SYSTEMS

FOR TWO EQUATIONS:
If a₁x + b₁y = c₁ and a₂x + b₂y = c₂
Δ = a₁b₂ – a₂b₁
x = (c₁b₂ – c₂b₁)/Δ
y = (a₁c₂ – a₂c₁)/Δ

✨ APPLICATIONS:

GEOMETRY PROBLEMS (LINE INTERSECTIONS)

PHYSICS (FORCES, ELECTRICAL CIRCUITS)

ECONOMICS (SUPPLY AND DEMAND EQUILIBRIUM)

ENGINEERING & COMPUTER SCIENCE

✅ FORMULAS TO REMEMBER:

ELIMINATION FORMULA: a₁b₂ – a₂b₁ ≠ 0 (UNIQUE SOLUTION)

IF a₁/a₂ = b₁/b₂ = c₁/c₂ → INFINITE SOLUTIONS

IF a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → NO SOLUTION

💡 RELATED KEYWORDS: SIMULTANEOUS EQUATIONS, LINEAR EQUATIONS, ALGEBRA, SUBSTITUTION METHOD, ELIMINATION METHOD, CRAMER’S RULE, GRAPHICAL METHOD, MATRIX METHOD, SYSTEMS OF EQUATIONS, DETERMINANTS, ALGEBRAIC SOLUTIONS, MATH OLYMPIAD, USA MATH, UK EXAMS, CANADA UNIVERSITY TESTS.

📌 TAGS: #MATH #ALGEBRA #SIMULTANEOUSEQUATIONS #ELIMINATION #SUBSTITUTION #CRAMERSRULE #USA #UK #CANADA #OLYMPIAD #UNIVERSITYEXAMS #MATHCHALLENGE