3x+y+z=3,2x+2y+5z+1=0,x=3y+4z+2
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MATHS
The number of solutions of the equation 3x+3y−z=5,x+y+z=3,2x+2y−z=3 is:
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The coefficient Matrix A is
A=
∣
∣
∣
∣
∣
∣
∣
∣
3
1
2
3
1
2
−1
1
−1
∣
∣
∣
∣
∣
∣
∣
∣
∣A∣=3[−1−2]−3[−1−2]−1[2−2]
=−9+9=0
Put x=0 in eq (1) eq (2)
3y−z=5
y+z=3.
4y=8
y=2,z=1
Now put this in equation (3)
x=0,
y=2
z=1.
⇒3=3
∴ Infinite solution
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so this question's answer is
x=1,y=1,and z=-1
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