Question

3z+5/2z+1=1/3,a is not equal to -1/2
​

Answer 1

Step-by-step explanation:

After making two zeros and expanding, we get

△=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

3

1

3

λ+2

1

−2

−3

∣

∣

∣

∣

∣

∣

∣

∣

=3(λ−5)

△

x

=

∣

∣

∣

∣

∣

∣

∣

∣

1

λ

2λ+1

1

3

2λ+2

1

−2

−3

∣

∣

∣

∣

∣

∣

∣

∣

=(λ−5)(λ+2)

△

y

=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

3

1

λ

2λ+1

1

−2

−3

∣

∣

∣

∣

∣

∣

∣

∣

=0

△

z

=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

3

1

3

λ+2

1

λ

2λ+1

∣

∣

∣

∣

∣

∣

∣

∣

=−(λ−1)(λ−5)

△=0 i.e, λ=5 the system has unique solution given by

△x

x

=

△

y

y

=

△

z

z

=

△

1

Hence the system has infinite solutions.

Putting λ=5 and eliminating z, we have 3x+5y=7 i.e only one equation in two variables.

Putting x=c,y=

5

7−3c

and hence from any z=−

5

2(1+c)

Answer 2

ANSWER:

11313λ+21−2−3∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣1λ2λ+1∣∣∣∣∣∣∣∣

△=1(−9+2λ+4)−1(−3+6)+1(λ+2−9)

△=2λ−5−3+λ−7

△=3λ−15

The given equations are

x+y+z=1⟶1

x+3y−27=λ⟶2

3x+(λ+2)y−3z=2λ+1⟶3

Irrespective of values of λ,x,y,z

From equation 1 we see that x+y+z=1

Answer:1

For all values of α, we find that x+y+z=1.