Find the x-intercept and the y-intercept for the graph of the equation. 3x y=-3

Let's start with simplifying this equation. Typically we have y = something, so let's rewrite it in this form.

3xy = -3

y = -3/3x

y = -1/x

Alright! Now, let's go ahead and solve for the y-intercept. Those only occur when x=0, so let's plug in 0 for x.

y = -1/0

Slight problem. Dividing by a 0 results in an imaginary number, or "undefined". In this case, there is no y-intercept.

Now we can solve for an x-intercept. These only occur when y=0, so let's set y to 0!

0 = -1/x

Well shoot! We have another problem. No regular number of x will give us a y=0. However, this problem isn't the same as our undefined one from before. Here, as x value approach infinity, we get closer and closer to 0. We can never actually hit 0, but we do approach it. I'm not sure how your teacher wants it answered, but strictly, there is no x-intercept. However, we can actually attempt to explain what is going on, which is that as x go to infinity, we APPROACH y=0.

Hope that helps, and please let me know if you need clarification on anything!

9514 1404 393

  30 small chairs and 24 large chairs

Step-by-step explanation:

Let x and y represent the numbers of small chairs and large chairs built in a day. Then the relations for using available time are ...

  20x +50y = 30×60

  60x +90y = 66×60

Removing common factors, these can be written in standard form as ...

  2x +5y = 180

  2x +3y = 132

Subtracting the second equation from the first gives ...

  2y = 48

  y = 24 . . . . . divide by 2

Using the first equation to find x, we have ...

  2x +5(24) = 180

  2x = 60 . . . . . . . . . . subtract 120

  x = 30 . . . . . . . . divide by 2

The company can build 30 small chairs and 24 large chairs in a day.