+0  
 
+1
127
4
avatar+809 

The lines \(x=\frac{1}{4}y+a\) and \(y=\frac{1}{4}x+b\) intersect at the point \((1,2)\). What is \(a+b\)?

 Aug 22, 2018
 #1
avatar+95358 
+3

Add the two together and then substitute.


\(x+y=0.25y+0.25x+a+b\\ Sub\;\; in\;\; x=1 \;\;and \;\; y=2\\ 1+2=0.5+0.25+a+b\\ 3=0.75+a+b\\ 2.75=a+b\\ a+b=2.75\)

.
 Aug 22, 2018
 #2
avatar+809 
+3

Thanks! But, 3-0.75=2.25. 

mathtoo  Aug 22, 2018
 #3
avatar+95358 
+2

Yes you are right :)  And so the answer shall be 2.25 

Melody  Aug 22, 2018
 #4
avatar+94558 
+2

x = (1/4)y + a               y  = (1/4)x + b

4x = y + 4a                  4y = x + 4b

y = (4x - 4a)                x  = (4y - 4b)

y = 4 ( x - a)                x = 4 ( y - b)

2 = 4( 1 - a)                 1  = 4 (2 - b)

(2/4)  = 1 - a               (1/4)  = 2 - b

(1/2)  = 1  - a                b = 2 - 1/4

a  = 1  -1/2                   b = 8/4 - 1/4

a  = 1/2                         b = 7/4

 

So...a +  b  =  1/2 + 7/4  =  2/4 + 7/4   =  9/4   

 

 

cool cool cool

 Aug 22, 2018

3 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.