Find solution of equations- Equations given

Chapter 4 Class 12 Determinants
Concept wise

### Transcript

Example 16 Solve the system of equations 2x + 5y = 1 3x + 2y = 7 Step 1 Write equation as AX = B [โ 8(2&5@3&2)] [โ 8(๐ฅ@๐ฆ)] = [โ 8(1@7)] A = [โ 8(2&5@3&2)] , X = [โ 8(๐ฅ@๐ฆ)] , B = [โ 8(1@7)] Step 2 Calculate |A|, A = [โ 8(2&5@3&2)] |A| = |โ 8(2&5@3&2)| = 2 ร 2 โ 5 ร 3 = 4 โ 15 = โ 11 Since |๐จ| โ  0, System is consistent and the system of equations has a unique solution AX = B X = A-1 B Step 3 Calculating X = A-1 B Here, A-1 = 1/(|A|) adj (A) adj A = [โ 8(2&5@3&2)] = [โ 8(2&โ5@โ3&2)] Now, A-1 = 1/(|A|) adj A Putting values = ๐/(โ๐๐) [โ 8(๐&โ๐@โ๐&๐)] & B = [โ 8(1@7)] Now X = A-1 B [โ 8(๐ฅ@๐ฆ)] = (โ1)/11 [โ 8(2&โ5@โ3&2)] [โ 8(1@7)] [โ 8(๐ฅ@๐ฆ)] = (โ1)/11 [โ 8(2(1)+(โคถ7โ5)7@โ3(1)+2(7))] [โ 8(๐ฅ@๐ฆ)] = (โ1)/11 [โ 8(2โ35@โ3+14)] = (โ1)/11 [โ 8(โ33@11)] = [โ 8(โ33 ร (โ1)/11@11 ร (โ1)/11)] [โ 8(๐ฅ@๐ฆ)] = [โ 8(3@โ1)] Hence x = 3 & y = โ 1

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.