Apet store currently has a total of 45 cats and dogs. there are 7 more cats than dogs. determine the number of cats and dogs in the store. write and solve a pair of simultaneous linear equation that represents the situation. interpret the solution.

x+y=45

x=y+7

Use substitution...

Plug y+7 into the first equation.  You get (y+7)+y=45.  Next combine the like terms.  2y+7=45.  Subtract 7 from both sides and you get 38.  Divide 2 on both sides to get y alone and you get 19.  Since there are more cats than dogs, this is the amount of dogs.  Add 19+7 since there are 7 more cats than dogs and you get 26 cats.  Therefore there is 19 dogs and 26 cats.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.