A paddock contains ducks and sheep. There are a total of 42 heads and 96 feet in the paddock. Determine how many ducks and how many sheep are in the paddock using simultaneous elimination.

Number of sheep and Number of duck are 6 and 36

Given that;

Number of total heads = 42

Number of total feet = 96

Find:

Number of ducks and sheep

Computation:

Number of legs in 1 sheep = 4

Number of legs in 1 duck = 2

So,

Assume;

Number of sheep = a

Number of duck = b

So,

a + b = 42 Eq1

4a + 2b = 96 Eq2

Eq2 / 2

2a + b = 48 Eq3

From Eq 3 and Eq1

a = 6

So,

b = 36

Number of sheep = 6

Number of duck = 36

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Number of ducks in paddock = 36

Number of sheep in paddock = 6

Step-by-step explanation:

Let d be the number of ducks and s be the number of sheep

Then according to given statements, the equations will be:

For elimination, multiplying equation 1 by 2 and then subtracting from equation 2:

Putting s = 6 in equation 1:

Hence,

Number of ducks in paddock = 36

Number of sheep in paddock = 6

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

h/o/e/s mad

step-by-step explanation:

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