This document provides a simple trick for solving two simultaneous linear equations in 3 steps: 1) Write the equations in the form a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0. 2) Use the formula to find x and y: x = (b1c2 - b2c1) / (a1b2 - a2b1) and y = (c1a2 - c2a1) / (a1b2 - a2b1). 3) Cross multiply the numbers in the boxes to solve for x and y, which for the example equations are x = 2 and y = -1

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

3. Visit our Blog for more SAT Helpful Insights and don't forget to share :)
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