Investigate for consistency of the following equations and if possible then find the solutions: 2x-3y+7z=5 3x+y-3z=13 2x+19y-47z=32

Dolly Robinson

Dolly Robinson

Answered question

2020-12-09

Investigate for consistency of the following equations and if possible then find the solutions:
2x-3y+7z=5
3x+y-3z=13
2x+19y-47z=32

Answer & Explanation

Anonym

Anonym

Skilled2020-12-10Added 108 answers

Step 1 
Think about the system of linear equations below:

2x−3y+7z=5 
3x+y−3z=13 
2x+19y−47z=32 
The equations should now be written in augmented matrix form:
[2375313132194732] 
Step 2 
D=|23731321947| 
=2|131947|(3)|33247|+7|31219| 
=2[1×(47)(3)×19]+3[3×(47)(3)×2]+7(3×191×2) 
=2(-47+57)+3(-141+6)+7(57-2) 
=2×10+3×(135)+7×55 
D=20 - 405 + 385 
=0 
Step 3 
Dx=|5371313321947| 
=5|131947|(3)|1333247|+7|1313219| 
=5[1×(47)(3)×19]+3[13×(47)(3)×32]+7(13×191×32) 
=5(-47+57)+3(-611+96)+7(247-32) 
=5×10+3×(515)+7×215 
Dx=501545+1505 
=10 
D=0 and Dx0
Hence, the system of equations is inconsistent. 
Hence, the system of equations has no solution.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-08Added 2605 answers

Answer is given below (on video)

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