# Thread: Determining the value of two variables so that two equations of a line are the same

1. ## Determining the value of two variables so that two equations of a line are the same

There are two equations. 3x+ky+2=0 and 5x-y+h=0. Determine the values of h and k so that the two equations are of the same line.

2. ## Re: Determining the value of two variables so that two equations of a line are the sa

Hey powercroat783.

For this one, the easiest way is that the two equations will be equal. So if you subtract one from the other you will get an equation that will be zero for all x and y which means that the coeffecients will also be equal to zero (of the equation that is the difference of the two).

So if you take one equation and minus it from the other, what can you conclude about the coeffecients?

3. ## Re: Determining the value of two variables so that two equations of a line are the sa

So you're saying to do 3x+ky+2=5x-y+h. Combining them as such would give me 2x-ky-y+h+2=0. The coefficients are 2 , -1 , -1, 1, and 2. I'm not sure what to conclude here, or if I even took your advice correctly.

4. ## Re: Determining the value of two variables so that two equations of a line are the sa

Sorry I should have pointed something out: You want to make the fixed co-effecients the same value and find the values of the other variables so that you get a perfect match.

Multiplying these equations by a constant does not change what they represent so multiply 3x + ky + 2 = 0 by 5/3 does not change what the equation represents.

5. ## Re: Determining the value of two variables so that two equations of a line are the sa

I don't follow. I want to match the coefficients so if I multiply 3x + ky + 2 = 0 by 5/3 I get 5x + 5ky/3 + 10/3 = 5x - y + h = 0

From this can I already conclude that k = -3/5 and h = 10/3?

6. ## Re: Determining the value of two variables so that two equations of a line are the sa

Yes, that's the idea.