Linear Equation

Simple Trickby using

Solve

8𝑥 + 5𝑦 = 11 → 8𝑥 + 5𝑦 – 11 = 0

3𝑥 – 4𝑦 10 → 3𝑥 4𝑦 10 = 0

Tricks

A

Let’s solve two simultaneous equations

First write coefficients of equation in form of presentation below

Now Formula goes like this

How to remember and use this method to solve equation within 30 Seconds

𝑎 𝑥 + 𝑏 𝑦 + 𝑐 = 0

𝑎 𝑥 + 𝑏 𝑦 + 𝑐 = 0

𝑥 (b₁c₂ − b₂c₁)(a₁b₂ − a₂b₁)

= 𝑁𝐷

𝑦 (c₁a₂ − c₂a₁)(a₁b₂ − a₂b₁)

= 𝑁𝐷

𝑎 1 𝑏 1 𝑐 1 𝑎 1

𝑎 2 𝑏 2 𝑐 2 𝑎 2

8 5 −11 8

3 −4 −10 3

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Now to find x and y, let’s divide the above boxes into three compartments and cross multiply numbers. Starting from left as shown below.

𝐷 8 ∗ (−4) − 5 ∗ 3 𝑁 1 = −5 ∗ (−10) − (−4) ∗ (−11) 𝑁 2 = −11 ∗ (3) − (−10) ∗ 8

𝐷 −32 − 15 ==

=

−47 𝑁 1 = −50 − 44 = −94 𝑁 2 = −33 + 80 = 47

So 𝑋 𝑁 1𝐷

−94−47

=== 2 𝑌 𝑁 2𝐷

−4747

== = −1

8 5 −11 8

3 −4 −10 3

8 5 −11 8

3 −4 −10 3

8 5 −11 8

3 −4 −10 3

𝑎 1 𝑏 1 𝑐 1 𝑎 1

𝑎 2 𝑏 2 𝑐 2 𝑎 2

𝑎 1 𝑏 1 𝑐 1 𝑎 1

𝑎 2 𝑏 2 𝑐 2 𝑎 2

𝑎 1 𝑏 1 𝑐 1 𝑎 1

𝑎 2 𝑏 2 𝑐 2 𝑎 2

Tricks