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Question

Find the number of solutions for the system of equations
4x + y + 2z = 5
x - 5y + 3z = 10
9x - 3y + 7z = 20

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Solution

4x + y + 2z = 5 … (1)
x - 5y + 3z = 10 x = 10 - 5y - 3z
9x - 3y + 7z = 20 … (2)
Eqn (1) becomes, 4(10 - 5y - 3z) + y + 2z = 5
40 - 20y - 12z + y + 2z = 5
-19y -10z = -35
19y + 10z = 35 … (3)
Eqn (2) becomes 9(10 - 5y - 3z) - 3y + 7z = 20
90 - 45y - 27z - 3y + 7z = 20
- 42y - 20z = - 70
21y + 10z = 35 … (4)
From (3) & (4),
19211010=3535 s/m of eqn has unique solution.
a1a2b1b2=c1c2 Unique solution. a1a2b1b2c1c2 no solution.
a1a2=b1b2=c1c2 Infinite solution.


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