Question

If 6x - 4xy= 5y(square root), find x when y=4
pls whole explanation write it in a way i can write on my test!

Answer 1

Answer:

What you have here are two equations:

x+y=5  [1]

xy=6  [2]

To solve for  x  and  y , you should rearrange one of the equations for one of the variables  x  or  y . Choose equation [1] to rearrange for  y , because it is easy to do so.

y=5−x  [3]

Now, substitute this expression into equation [2]:

x(5−x)=6  

Now use this equation to solve for  x . Firstly expand the parentheses:

5x−x2=6  

Rearrange the terms so that they are all on one side of the equation:

x2−5x+6=0  

What you have here is a quadratic equation. There are many ways to solve a quadratic equation but I will choose the easiest method for this problem.

Factorise the quadratic expression on the left-hand side of the equation by using the product-sum method (or by decomposition):

(x−2)(x−3)=0  

The null factor law gives  x=2  or  x=3  as the solution.

Now, substitute  x=2  or  x=3  into equation [3] to get the value of y:

when  x=2 , then  y=5−2=3  

when  x=3 , then  y=5−3=2  

Therefore, there are two solutions to these simultaneous equations, which are:  (2,3)  and  (3,2)  ■