Question

If x+y = 2; y+z = 3; z+x = 5, then what will be the value of x+y+z ?

Answer 1

x + y + z = 5

Step-by-step explanation :

1. Easy way :

Given,

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

Adding the above equations, we get

x + y + y + z + z + x = 2 + 3 + 5

or, 2 (x + y + z) = 10

or, x + y + z = 5

Therefore the value of x + y + z is 5.

2. By finding values :

Given,

x + y = 2 ..... (1)

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

z + x = 5 ..... (3)

Now, (3) - (2) gives

z + x - y - z = 5 - 3

or, x - y = 2 ..... (4)

Now, (2) + (4) gives

x + y + x - y = 2 + 2

or, 2x = 4

or, x = 2

Then y = 2 - 2

i.e., y = 0

Also z = 5 - 2

i.e., z = 3

Therefore, x + y + z = 2 + 0 + 3 = 5 .

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if x+y+z=9 and xy+yz+zx=26 - https://brainly.in/question/3756412

Answer 2

The value of x+y+z = 5

Given,

x+y = 2;

y+z = 3;

z+x = 5

Adding all the above equations, we get,

x+y + y+z + z+x = 2 + 3 + 5

2x + 2y + 2z = 10

2 (x + y + z) = 10

x + y + z = 10/2

∴ x + y + z = 5