equations invlving fractions

[Traci-Ann]

Hello, I am taking an online college math class over the summer, and 4 days later my teacher still hasn't answered my question about the assigment.

I am struggling with questions that look like this

find two solutions for each equation

3/4x - 2/5y = 6

It has been a good 20 years since I have had a math class. I know at one time I knew how to do this, but now I am struggling with the fractions. I do not remember if I need to reduce them, factor them, find a common demintor. I just keep looking and thinking I am missing a step, but I do not remember what that step is. If someone could walk me through the steps here, I think I could figure out the other 8 equations that are fractions.

Thanks in advance!

 

[galactus]

The thing to do is sub in any value for x, then solve for y.

Pick anything for x. Say, 4

\(\displaystyle \frac{3(4)}{4}-\frac{2y}{5}=6\)

\(\displaystyle 3-\frac{2y}{5}=6\)

Subtract 3:

\(\displaystyle \frac{-2y}{5}=3\)

Multiply by 5:

\(\displaystyle -2y=15\)

\(\displaystyle y=\frac{-15}{2}\)

There's one.

Next, choose another value for x and solve for y again. That's it. You have the two values for x and y.

 

[Traci-Ann]

So you timed the -2y/5=3 by 5 on each side to get the whole number? That is the step I think I got lost on. I was trying to work with fractions. Thank You

 

[Denis]

3/4x - 2/5y = 6

Good idea to rewrite these this way: 3x / 4 - 2y / 5 = 6

Now you can clearly see the denominators as 4 and 5; now multiply each by 20:
15x - 8y = 120 ; much easier to handle, right?