Question

Solve the following systems of equations x+y=3 ; y+z=6 ; x+z=5.

Answer 1

x = 1

y = 2

z = 4

Explanation:

Given equations

x + y = 3

or

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

y + z = 6 .................(2)

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

substituting 1 in equation 3, we get

( 3 - y ) + z = 5

or

3 - y + z = 5

or

z = 2 + y ...............(4)

now,

substituting 4 in equation 2, we get

y + ( 2 + y ) = 6

or

2 + 2y = 6

or

2y = 4

or

y = 2

substituting value of y in equation 4 we get

z = 2 + 2 = 4

and substituting value of y in equation 1 we get

x = 3 - 2 = 1

thus,

x = 1

y = 2

z = 4