SOLUTION: 1. 3x + y = 6 x - y = 1 2. If x Varies directly as y^2, and x= 20 when y= 2, find x when y= 10.

Algebra ->  Linear-equations -> SOLUTION: 1. 3x + y = 6 x - y = 1 2. If x Varies directly as y^2, and x= 20 when y= 2, find x when y= 10.      Log On


   

Question 73404This question is from textbook
: 1. 3x + y = 6
x - y = 1
2. If x Varies directly as y^2, and x= 20 when y= 2, find x when y= 10. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

    3x + y = 6
     x - y = 1

Add the 2 equations. Add 3x to x, y to -y, and 6 to 1

    4x     = 7

Now solve for x
4x=7
x=7%2F4
Plug this into x-y=1
%287%2F4%29-y=1
-y=1-%287%2F4%29
-y=%284-7%29%2F4
-y=-3%2F4
y=3%2F4
Check:

    3(7/4) + 3/4 = 6
      7/4 - 3/4 = 1
                     


    21/4 + 3/4 = 6
      4/4 = 1
                     


    24/4 = 6
      1=1 Works
                     


      6 = 6 Works
      1 = 1 Works


Since x varies directly as y^2, the equation looks like
y%5E2=kx
So just plug in x=20 and y=2 to find k
2%5E2=k%2A20
4%2F20=k
k=1%2F5
Now plug k into the equation to find x when y=10
y%5E2=%281%2F5%29x
10%5E2=%281%2F5%29xPlug in y=10
5%2A10%5E2=x
x=500