Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Solve system of linear equations, using matrix method. 5x + 2y = 3, 3x + 2y = 5.

Q : 10       Solve system of linear equations, using matrix method.

                 \small 5x+2y=3

                \small 3x+2y=5

Answers (1)

best_answer

The given system of equations

 \small 5x+2y=3

 \small 3x+2y=5

can be written in the matrix form of AX =B, where

A = \begin{bmatrix} 5 &2 \\ 3& 2 \end{bmatrix}, X = \begin{bmatrix} x\\y \end{bmatrix}  and B = \begin{bmatrix} 3\\5 \end{bmatrix}

we have, 

|A| = 10-6=4 \neq 0.

So, A is non-singular, Therefore, its inverse A^{-1} exists.

as we know A^{-1} = \frac{1}{|A|} (adjA)

A^{-1} = \frac{1}{|A|} (adjA) = \frac{1}{4}\begin{bmatrix} 2 &-2 \\ -3& 5 \end{bmatrix}

So, the solutions can be found by X = A^{-1}B = \frac{1}{4}\begin{bmatrix} 2 &-2 \\ -3 & 5 \end{bmatrix}\begin{bmatrix} 3\\5 \end{bmatrix}

\Rightarrow \begin{bmatrix} x\\y \end{bmatrix} = \frac{1}{4}\begin{bmatrix} 6-10\\ -9+25 \end{bmatrix} = \frac{1}{4}\begin{bmatrix} -4\\16 \end{bmatrix}= \begin{bmatrix} -1\\4 \end{bmatrix}

Hence the solutions of the given system of equations;

x =-1 \ and\ y =4.

Posted by

Divya Prakash Singh

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question