Question 11175
Let the weight of the 1st chicken = x, the weight of the 2nd = y, and the weight of the 3rd = z.

1) {{{x + y = 10.6}}}
2) {{{y + z = 8.5}}}
3) {{{x + z = 6.1}}}

Now we need to solve for x, y, and z.  We have a system of three equations with three unknowns.

Let's rewrite two of the three equation and substitute into the third one.

1) {{{x + y = 10.6}}} rewrite as: {{{x = 10.6 - y}}}
2) {{{y + z = 8.5}}} rewrite as: {{{z = 8.5 - y}}}  Substitute these into the 3rd equation and solve for y.

3) {{{x + z = 6.1}}} or
 {{{(10.6 - y) + (8.5 - y) = 6.1}}} Simplify and solve for y.

{{{19.1 - 2y = 6.1}}} Add 2y to both sides.
{{{19.1 = 2y + 6.1}}} Subtract 6.1 from both sides.
{{{13 = 2y}}} Divide both sides by 2.
{{{y = 6.5}}}

From the rewritten equation 1):

{{{x = 10.6 - y}}}
{{{x = 10.6 - 6.5}}}
{{{x = 4.1}}}

From the rewritten equation 2):

{{{z = 8.5 - y}}}
{{{z = 8.5 - 6.5}}}
{{{z = 2}}}

The chickens weigh 4.1 kgs, 6.5 kgs, and 2 kgs.

The three chickens would together, weigh x + y + z or 4.1 + 6.5 + 2 = 12.6 kgs.