Question

A pet 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.

Answer 1

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.