Question

x+y+z=6 , x-y+2z=5 , 3x+y+z=8 solve it​

Answer 1

Answer:

X =1

Y = 2

Z = 3

Step-by-step explanation:

x+y+z=6 , x-y+2z=5

then x+y+z = x - y + 2z + 1

    y + z = 2z-y+1      

  y = z-y+1

2y = z+1  

y = z+1/2           .....(1)

x-y+2z=5 , 3x+y+z=8

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

z-y+3 = 2x+y

2y = z-2x + 3

y  = z-2x+3/2   ....(2)

z+1/2 =  z-2x+3/2     ( joining (1) and (2))

z + 1 =  z-2x+3

z = z - 2x+2

0 = 2-2x

-2 = -2x

x = -2/-2 = 1    ****************************X

x+y+z=6

y+z = 6-1 = 5   ...(3)

joining (3) and (1)

y + z = 5       ...using(3)

(z+1)/2 + z = 5   ...using (1)

(z+1+2z)/2 = 5

3z+1 = 5*2 = 10

3z =10-1 = 9

z= 9/3 = 3    ***************************Z

back to (3)we can see

y+z = 5

y + 3 = 5

y = 5-3 = 2 ****************************Y

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Answer 2

x = 1 , y = 2 and z = 3  if +y+z=6 , x-y+2z=5 , 3x+y+z=8

Given:

• x+y+z=6          Eq1
• x-y+2z=5        Eq2
• 3x+y+z=8       Eq3

To Find:

• Values of x , y and z

Solution:

Step 1:

Subtract Eq1 from Eq3   and solve for x

( 3x+y+z) -(x + y + z) = 8 - 6

2x  = 2

=> x = 1

Step 2:

Add Eq 1 and Eq2

(x + y + z) + (x - y + 2z) = 6 + 5

2x + 3z = 11

Step 3:

Substitute x = 1 and solve for z

2(1) + 3z = 11

=> 3z = 9

=> z = 3

Step 4:

Substitute x = 1  and z = 3 in Eqi and solve for y

1 + y + 3 = 6

=> y + 4 = 6

=> y = 2

Hence  x = 1 , y = 2 and z = 3