Question

show that the equations x+2y-z=3,3x-y+2x=1,2x-2y+3z=2,x-y+z=-1 are consistent and solve them ?​

Answer 1

Answer:

help

Step-by-step explanation:

Answer 2

Answer:

The values of x, y and z are -2, 6 and 7 respectively.

Step-by-step explanation:

Given:

x+2y-z=3

3x-y+2z=2

x-y+z=-1

To find:

Consistency of the equations and values of x,y and z.

Solution:

x+2y-z=3        ................................(1)

3x-y+2z=2      ................................(2)

x-y+z=-1          .................................(3)

Firstly, we have to determine the consistency of the equations.

For that we have to write the coefficients of the equations in the form of a matrix and solve it.

= 1(-1+2)-2(3-2)-(-3+1)

= 1(1)-2(1)-1(-2)

= 1-2+2

= 1 ≠ 0

So, the equations have an unique solution.

Now, we have to solve the equations.

Now, we have to solve the equations.

On solving equation 3 further we get,

x=y-z-1          ..............................(4)

Now, put equation 4 in equation 1 and 2.

y-z-1+2y-z=3

3y-2z=4         .................................(5)

3x-y+2z=2

3(y-z-1)-y+2z=2

3y-3z-3-y+2z=2

2y-z=5                 ....................................(6)

Multiply 2 with equation 5 and 3 with equation 6 and subtract them.

6y-3z=15

(-)  (-)   (-)

6y-4z=8

     z=7

Now, put the value of z in equation 6.

2y-7=5

2y= 12

y= 6

Similarly, put the values of z and y in equation 3.

x-6+7=-1

x+1= -1

x= -1-1

x= -2

Therefore, the values of x, y and z are -2, 6 and 7 respectively.

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