For what values of $y$ does the following equation have no solutions for $x$?

$$xy + 5y + 4x + 20=1.$$

Thanks4helping Nov 16, 2020

#1**+1 **

1) You have to leave all the terms with an x it it on the left side and take all the other terms to the other side.

2) You have to factorize the left side.

3) You have to to get x by it self on the left

4) you cannot divide by 0

Do as much of that as you can and then show us what you have done.

**No one else answer over me. Thank you.**

Melody Nov 16, 2020

#3**+1 **

If we look at xy + 5y, we see that both terms share a factor of y . This gives me y(x + 5) + 4x + 20 = 1

Similarly,4x and 20 do share a factor of 4 , giving me y(x + 5) + 4x(x + 5) = 1

these two terms have a factor of x + 5 , so (y + 4)(x + 5) = 1

Dividing both sides by y + 4 and subtract both sides by to get x = 1/y + 4 - 5 am I right?

Thanks4helping
Nov 16, 2020

#5**+1 **

I'll take a look

\(xy + 5y + 4x + 20=1. \)

If we look at xy + 5y, we see that both terms share a factor of y . This gives me y(x + 5) + 4x + 20 = 1 **correct**

Similarly,4x and 20 do share a factor of 4 , giving me y(x + 5) + 4x(x + 5) = 1

**No ** 4x(x+1)=4x^2+4x and there are no squared terms in this problems.

y(x + 5) + 4x + 20 = 1

You need to get the 4x and the 20 onto the other side. How do you do that?

After you do that you will be up to my number 3).

3) You have to to get x by it self on the left

4) you cannot divide by 0

Do as much of that as you can and then show us what you have done.

Melody Nov 16, 2020

#7**+1 **

x ( y + 4) + 5 ( y + 4) = 1 (x + 5) (y + 4) = 1 and divide both sides by (y + 4) right

Thanks4helping
Nov 17, 2020

#8**+2 **

No that is not right. But I am glad to see that you are trying to answer me.

Mz instructions

y(x + 5) + 4x + 20 = 1

You need to get the 4x and the 20 onto the other side. How do you do that?

I should not really work it as putting them on the other side. (Although it is common working and that is what happens)

But what I am really asking you to do is get 4x and 20 OFF the left side.

at the moment you have +4x so you will have to take 4x away. +4x-4x = 0

you also have +20 so you will need to take that away too 20-20 = 0

So the left side will be

y(x + 5) + 4x + 20 - 4x - 20

BUT equations must stay BALANCED.

If you do something to one side you must do it to the other side as well. Otherwise the scale will tip sideways.

so this is what you have to do.

y(x + 5) + 4x + 20 = 1

y(x + 5) + 4x + 20-4x-20 = 1-4x-20

Now simplify both sides and then get back to me with your answer. Leave the y(x+5) alone for the moment.

----------------------------------------

**After** you do this tell me what is the invisible symbol between y and (x+5)

And

what is the opposite operation to that. Like the opposite of + is - because +4-4 = 0

Melody
Nov 17, 2020