Copland completes in 27 swimming events this season. He wins either first place or second place in each event. Copland has 3 more first place wins than second place wins. In how many events did he wins first place, and in how many did he win second place.

First Place wins in 15 events

Second Place wins in 12 events

Step-by-step explanation:

Let

the number of events winning first place be "f"

the number of events winning second place be "s"

Total 27 swimming events, we can write:

First place wins is THREE MORE than 2nd place wins, so we can write:

Replacing 2nd equation in 1st equation, we can solve for "s":

We know

f = s + 3

so,

f = 12 + 3

f = 15

Thus,

First Place wins in 15 events

Second Place wins in 12 events

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

hi! i think the answer is 1/2 : )