Easier Than You Think: Mastering System of Equations with Ease!

Easier Than You Think: Mastering System of Equations with Ease!

🔍 Don't let complex equations intimidate you! Join me on a journey to mastering systems of equations with ease. In this tutorial, we'll break down the process step-by-step, revealing simple techniques that make solving these equations a breeze. Whether you're a beginner or just need a refresher, this video will boost your confidence and empower you to tackle any system of equations with ease!

Topics covered:
System of equations
Algebra
Cubic equation
Algebraic identities
Algebraic manipulations
Vieta's Method
Solving systems of equations
Synthetic division method
Rational root theorem
Math tutorial
Math Olympiad
Math Olympiad Preparation

Timestamps:
0:00 Introduction
1:01 Algebraic identities
2:40 Solving systems of equations
3:44 Substitution
8:22 Quadratic equation
9:04 Factorization
10:45 Solutions

#mathtutorial #systemofequations #mathhelp #problemsolving #mathematics #algebra #learnmath #mathisfun #youtubetutorial #mathematicseducation

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Thanks for watching!
@infyGyan

[SidneiMV]

awesome solution Sir. congratulations.

[woobjun]

Simplifications of the given were great, sir!

[SidneiMV]

(x + y)² = x² + y² + 2xy
x² + y² = (x + y)² - 2xy

x + y = a
xy = b

a² - 3b = 61/a
3b = a² - 61/a

a + b = -18/a - 1
b = -(a + 1 + 18/a)

a² - 61/a = -3(a + 1 + 18/a)
a³ - 61 = -3a² - 3a - 54
a³ + 3a² + 3a - 7 = 0
(a + 1)³ = 8
a = 1

3b = a² - 61/a = 1 - 61 = -60
b = -20

x + y = 1
xy = -20

t² - 1t - 20 = 0
(t - 5)(t + 4) = 0

*(x, y) = {(5, -4); (-4, 5)}*

[RashmiRay-cy]

Let x+y =a and xy = b. Then, a^2-3b=61/a and a+b = -18/a -1. > b = -a -18/a -1. Eliminating b, we get a^3 + 3a^2 + 3a -7 = 0. The only real solution is a=1 > b = -20. So, y = -20/x. Thus, x - 20/x = 1 > x^2 -x -20 =0 > (x, y) = (5, -4), (-4, 5).

[Bertin-qy]

(-4;5) (5;-4) .tout le reste est complexe

[victorchoripapa]

Well... I think that won't be easy to solve but...
Having some fun would be awesome