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4x=3y+7;x=4,5,6

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4 Answers

Essentially you are given an equation 4x = 3y +7,    and that x= 4,5,6   but are given no other info.

Well you sort of have to guess what they want you to do.  Usually in math they want you to solve for things.  Well you are given values for x.  Since we already know what the x's are most likely they want to know what value the y's are.

It seems like this is just one question but in fact it is three questions.

One way to answer the question is to plug these x values in one at a time and find y.

So  when x=4   4*4 = 3y + 7   gives   16 = 3y + 7     subtract 7 both sides

16-7  = 3y + 7 - 7---->   9 = 3y     divide by coefficient on y    9/3  = 3y/3  ---> 3 = y

So the first solution is ordered pair (x,y) = (4,3)  Now instead of doing this every single time it might be easier to solve the original equation in terms of y

4x = 3y  + 7    subtract 7

4x - 7 =  3y     divide by 3

(4x - 7)/3  = 3y/3  giving equation

y = (4x-7)/3      So no we can plug the other two x's more easily without performing the same operations everytime

For x = 5    y = (4*5-7)/3    = (20 - 7)/3  = 13/3   so solution is (5,13/3)

For x = 6    y  = (4*6 - 7)/3  = (24 - 7)/3  = 17/3  so solution is (6, 17/3)

In math we denote the y variable as a convinent way of representing f(x). So this implies that y is dependent on x, or simply y  = f(x). Thus, the goal here is to rearrange what was given in this form. So, we here given  

4x  = 3y +7  ;x = 4,5,6 

Step 1)  subtract 7 from both sides since we are dealing with equality, then we have

4x -7 = 3y 

Step 2) Divide by 3 from both sides

(4x - 7)/3 = y 

Here, we have f(x) = (4x - 7)/3 = y. So now we were given x values in which we have to evaluate using our new function y = f(x). So, the following is the answer: 

 

y = f(4) = (4(4) -7)/3 = (16 -7)/3 = (9)/3 = 3

y = f(5) = (4(5) -7)/3 = (20 -7)/3 = (13)/3 = 13/3

y = f(6) = (4(6) -7)/3 = (24 -7)/3 = (17)/3 = 17/3

 

In essence a function is a type of relation in which has certain characteristics. Here, we can take your given x values and apply the function y = f(x) and form a graph by plotting points containing the coordinates (x,y).  For example, to plot what you have for y above we get points, 

(4, 3)

(5, 13/3)

(6, 17/3) 

You will learn more about all this pretty soon if you haven't already. 

You are given the equation     4x = 3y + 7 ,   which has two unknown variables x and y.

Since you are given specific values for one of the unknown variables (x), then your goal is to use these values of the variable x to find what the other unknown variable (y) is for each value of x given.

That said, solve the equation for the unknown variable y so that all you would have to do is plug in each value of x given to generate a y value.

   4x = 3y + 7                    

                       subtract 7 from both sides of the equation

   4x - 7 = 3y + 7 - 7      ==>      4x - 7 = 3y    

                       divide both sides of the equation by 3

   (4x - 7) / 3 = (3y) / 3      ==>      (4x - 7)/3 = y

You now have the following equation:     y = (4x - 7)/3

And you are given the following values of x:     x = 4, 5, 6 

Find the value of y for each value of x:

1.) x = 4 ,     y = (4x - 7)/3 = (4(4) - 7)/3 = (16 - 7)/3 = (9)/3 = 3

2.) x = 5 ,     y = (4(5) - 7)/3 = (20 - 7)/3 = (13)/3 = 13/3 

3.) x = 6 ,     y = (4(6) - 7)/3 = (24 - 7)/3 = (17)/3 = 17/3

You have to solve for y if x is 4, 5, or 6. Substitute each one of those three different numbers in the equation and solve for each. Let's do 1, 3, and 3, and then you can solve for 4,5, 6.

If x = 1, 4x=3y becomes 4x1 = 3y, 4x1 = 4, so 4 = 3y, or 3y = 4. Divide each side by 3 to get read of the three by the y: 3y/3 = 4/3. The 3's on teh left cancel each other out, so y = 4/3 (or 1 1/3, or 1.333333.......)

If x = 2: 4x2=3y, or 3y = 4x2 (having the unknown on the left makes it easier ot read). 3y = 8. Divide each side by 3: 3y/3 = 8/3. y = 8/3, or 2 2/3, or about 2.6667.

If x = 3: 3y = 4x3. 3y = 12. y = 4 (dive each side by 3).

SO ... if x = 1,2,3 respectively, then y = 4/3, 8/3, 4, respectively. Now you can solve for 4, 5, 6! :-)