Jeri has a total of 40 pets with a total of 160 legs. If she owns only cats and dogs, how many of each does
she have? Write a system of equations to represent
this situation. Solve it using any method.

let x be the number of cats and y be the number of dogs:

x + y = 40

4x + 4y = 160

If you divide both sides of the second equation by 4, you will be left with:

x + y = 40

Then, subtract both equations:

x + y =40

- (x + y = 40)

0 = 0

Since you have a number = a number, there are infinite solutions.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0