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If the system of linear equations 

2x+2y+3z=a

3x-y+5z=b

x-3y+2z=c

where a,b,c are non-zero real numbers, has more than one solution, then :

  • Option 1)

     

    b-c-a=0

  • Option 2)

     

    b+c-a=0

  • Option 3)

     

    b-c+a=0

  • Option 4)

     

    a+b+c=0

Answers (1)

best_answer

 

Non-homogeneous system of linear equation -

b\neq 0

- wherein

 

 

Solution of a system of equations -

x_{1},x_{2},\cdot \cdot \cdot ,x_{n} satisfy the system of linear equations  Ax=B

- wherein

 

 

Consistent system of linear equation -

If the system of equations has one or more solutions 

-

 

For these 3 equations having more than 1 solution

\Rightarrow D=0

\Rightarrow \begin{vmatrix} 2 &2 &3 \\ 3 & -1 &5 \\ 1&-3 &2 \end{vmatrix}=0

\Rightarrow 26-20-24=0

\Rightarrow D=0

Also, D_{1}=D_2=D_3=0

D_1= \begin{vmatrix} a &2 &3 \\ b & -1 &5 \\ c&-3 &2 \end{vmatrix}=0

\Rightarrow a\left ( 13 \right )-b\left ( 13 \right )+c\left ( 13 \right )=0

\Rightarrow a-b+c=0

D_2= 0\Rightarrow \begin{vmatrix} 2 &a &3 \\ 3 & b &5 \\ 1&c &2 \end{vmatrix}=0

\Rightarrow a-b+c=0

D_3= 0\Rightarrow \begin{vmatrix} 2 &2 &a \\ 3 &-1 &b \\ -1&-3 &c \end{vmatrix}=0

\Rightarrow a-b+c=0

 


Option 1)

 

b-c-a=0

Option 2)

 

b+c-a=0

Option 3)

 

b-c+a=0

Option 4)

 

a+b+c=0

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