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

mathtoo  Aug 22, 2018
 #1
avatar+93920 
+3

Add the two together and then substitute.


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

Melody  Aug 22, 2018
 #2
avatar+621 
+3

Thanks! But, 3-0.75=2.25. 

mathtoo  Aug 22, 2018
 #3
avatar+93920 
+2

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

Melody  Aug 22, 2018
 #4
avatar+91381 
+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

CPhill  Aug 22, 2018

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