Expert answers to "Solve the systems of equations using matrices. 4x+5y=8..."

smileycellist2

Answered question

2021-02-05

Solve the systems of equations using matrices.

4 x + 5 y = 8

3 x - 4 y = 3

Leave answer in fraction form.

4 x + y + z = 3

- x + y = - 11 + 2 z

2 y + 2 z = - 1 - x

Answer & Explanation

pierretteA

Skilled2021-02-06Added 102 answers

Step 1
The given equation
$4 x + 5 y = 8$
$3 x - 4 y = 3$
In matrix form
$[\begin{matrix} 4 & 5 \\ 3 & - 4 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 8 \\ 3 \end{matrix}]$ $A X = B$

Step 2

$X = A^{- 1} B A = [\begin{matrix} 4 & 5 \\ 3 & - 4 \end{matrix}] A^{- 1} = \frac{1}{- 16 - 15} [\begin{matrix} - 4 & - 5 \\ - 3 & 4 \end{matrix}] = \frac{- 1}{31} [\begin{matrix} - 4 & - 5 \\ - 3 & 4 \end{matrix}]$
$B = [\begin{matrix} 8 \\ 3 \end{matrix}]$
Step 3
$A^{- 1} B = \frac{- 1}{31} [\begin{matrix} - 4 & - 5 \\ - 3 & 4 \end{matrix}]$ $[\begin{matrix} 8 \\ 3 \end{matrix}]$
$= \frac{- 1}{31} [\begin{matrix} - 47 \\ - 12 \end{matrix}]$
$x = \frac{47}{31}$
$y = \frac{12}{31}$

Jeffrey Jordon

Expert2022-01-29Added 2575 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?

Product

Company

Connect with us

Get Plainmath App

Google Play

Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus

Cyprus reg.number: ΗΕ 419361

E-mail us: support@plainmath.net

Our Service is useful for:

Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples. Plainmath.net is owned and operated by RADIOPLUS EXPERTS LTD.