If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:5:01

CCSS.Math: , , , ,

farmer Jan is a vegetable farmer who divides his field between broccoli crops and spinach crops last year he grew six tons of broccoli per acres of six tons of broccoli per acre and nine tons of spinach nine tons of spinach per acre for total of 93 tons of vegetables this year he grew two tons of broccoli per acre so this year he grew two tons of broccoli per acre and three tons of spinach per acre and three tons of spinach breaker for a total of 31 tons of vegetables how many acres of broccoli crops and how many acres of spinach crops does farmer Jan have so let's think about this so let's say that the number of acres of broccoli crops let's call that let's call that B and let's say the acres of spinach crops acres of spinach crops let's call that s so how much how much broccoli is he going to grow in I guess you could say last year last year how much broccoli did he grow and let me just write this down this is last year last last year and they tell us last year he grew six tons of broccoli per acre so if he grew six tons of broccoli per acre and he has B acres well that means he grew six tons per acre times B acres so he grew six B tons of broccoli last year and by the same logic he grew how much spinach well nine tons of spinach per acre times s acres so 9 s tons of spinach and then the total is 93 tons so for a total of 93 tons of vegetables so this is going to be equal to 93 so now let's think about this year and in general when you tackle these just think about well set the variables in general to what they're asking for and then how can you use the information that they're giving us so this year how much broccoli would he have grown well he grew two tons of broccoli per acre so he grew two tons per acre he has the same number of acres we can assume that so two tons per acre times B acres is going to be to be tons of broccoli and by that same logic it's going to be he grew three tons of spinach per acre well he has s acres each of those acres he's growing three tons of spinach per acre so it's going to be 3 s tons of spinach and they tell us what that total is that total is for a total of 31 tons of vegetables so this is going to be equal to 31 and so now we have a system of two equations with two unknowns that we can use to solve for B and s so let's see what do we want to solve for first well what we could do let me rewrite the top equation so we have 6 B plus + 9 s is equal to 93 is equal to 93 and the second equation well I doubt let's try to eliminate let's try to eliminate the B's so let's multiply the second equation by negative 3 so negative I'm going to multiply the left-hand side by negative 3 and I'm going to multiply the right-hand side by negative 3 and so what I'm going to what am what am I going to get negative 3 times 2 B is negative 6 B that was the whole point by multiplying it by negative 3 negative 3 times 3 s is negative 9 s negative 9 s and then negative 3 times 31 is going to be negative 93 so what do we get if we now add the two sides of this of these equations so on the left-hand side 6 B minus 6 B that's 0 9 s minus sinus that's 0 we're going to get just 0 on the right-hand side we get 93 minus 93 well that's still just going to be 0 so we have the situation where we get 0 equals 0 which is going to be true no matter what x and y are and so this is a system with an infinite number of solutions so this has infinite infinite infinite number of solutions so one way we could think about it is these two constraints they're not giving us enough information there's an infinite number of B and s combinations that would satisfy these equations so they're not giving us enough information to say how exactly what B and s are so there is not enough not enough info but an exclamation mark there