A simple trick to solve the Linear Equation problems for competitive exams like SAT, ACT, PSAT etc.

1. LinearEquation
Simple Trick
by using
Solve

2. 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)
=
𝑁
𝐷
𝑦
(c₁a₂ − c₂a₁)
(a₁b₂ − a₂b₁)
=
𝑁
𝐷
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 1
𝐷
−94
−47
=== 2 𝑌
𝑁 2
𝐷
−47
47
== = −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