homework help? : )?

Question

ok, so im doing linear equations in math and we had a sub. today who didn't bother to explain anything and was pretty pissy so i decided not to ask questions. anyone know how to do these? ex. 3x=5y and 3/x + 4/y =2 has something to do with moving around the numbers/letters. please.

Answer 1

Okay, you have two equations and two unknowns:

3x=5y
3/x + 4/y = 2

Now, we need to find values of x and y such that both of these equations are satisfied at the same time. What you do in these situations is to first solve for one of the variables, say, x, in terms of y in one of the equations. Then you can substitute that value for x into the other equation, so it becomes an equation only in y . After solving that equation for y (you will get a number), you can find the value of x by plugging it back into the first equation. For this instance, I'll start by solving the first equation for x:

x=5y/3

That was easy. Now I know what x is in terms of y, so I will substitute this into the second equation:

3/(5y/3) + 4/y = 2

Now, I need to solve for y. First I multiply both sides by y to get:

3/(5/3) + 4 = 2y
9/5 + 4 = 2y
29/5 = 2y

Dividing by 2 yields:

y=29/10

Now plugging this into the first equation I get:

3x = 5(29/10) = 29/2
x=29/6

So our answer is x=29/6, y=29/10

Answer 2

well, if you have 3x=5y and you want y by itself then you would divide both sides of the equation by 5. This would give you y=3/5x. If you want to graph that as a line you would start at point (0,0) and go up 3 and right 5. The second equation also needs to get y by itself. For that you would move 3x over to the other side of the the = sign. This would give you 4/y= -x/3+2. Now you would multiple both sides by 4 giving you y= -4/3x+8. Start at (0,8) and go down 4 and right 3. That gives you the graphs of both of those lines. I'm not sure if that's what you're looking for, but oh well, at least you know the lines now. :)