Best solutions to - "Using matrix method solve the following simultaneous equations..."

High School
Algebra
Algebra I
Quadratic function and equation

vetrila10

Answered question

2021-12-07

Using matrix method solve the following simultaneous equations

2 x + 3 y = 13

x - 4 y = 1

Answer & Explanation

Tamara Donohue

Beginner2021-12-08Added 11 answers

Step 1
Given System of equations can be written as
$A X = b$
$A = [\begin{matrix} 2 & 3 \\ 1 & - 4 \end{matrix}], X = [\begin{matrix} x \\ y \end{matrix}] a n d b = [\begin{matrix} 13 \\ 1 \end{matrix}]$
$\Rightarrow [\begin{matrix} 2 & 3 \\ 1 & - 4 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 13 \\ 1 \end{matrix}]$
$R_{2} r i g h t \Rightarrow R_{1}$
$\Rightarrow [\begin{matrix} 1 & - 4 \\ 2 & 3 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 1 \\ 13 \end{matrix}]$
$R_{2} \Rightarrow R_{2} - 2 R_{1}$
$\Rightarrow [\begin{matrix} 1 & - 4 \\ 0 & 11 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 1 \\ 11 \end{matrix}]$
$R_{2} \Rightarrow \frac{1}{11} R_{2}$
$\Rightarrow [\begin{matrix} 1 & - 4 \\ 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 1 \\ 1 \end{matrix}]$
$R_{1} \Rightarrow 4 R_{1} + R_{2}$
$\Rightarrow [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 5 \\ 1 \end{matrix}]$
$x = 5, y = 1$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Algebra I

Didn't find what you were looking for?