Do these in your head

Algebra Level 2

Solve the system of equations:

271x + 229y = 771

229x + 271y = 729

x = 229/271, y = 271/229 None of the other choices are the correct solution x = 750/229, y= 750/271 x = 1, y = 2 x = 2, y = 1

Denton Young by Denton Young , 47, USA

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2 solutions

271 x + 229 y = 771 \displaystyle 271x+229y=771 and 229 x + 271 y = 729 \displaystyle 229x+271y=729

Term 1

⇒ 271 x + 229 y + 229 x + 271 y = 771 + 729 \Rightarrow 271x+229y+229x+271y=771+729

⇒ 500 ( x + y ) = 1500 ⇒ x + y = 3 \Rightarrow 500(x+y)=1500 \Rightarrow x+y=3

Term 2

⇒ 271 x + 229 y − 229 x − 271 y = 771 − 729 \Rightarrow 271x+229y-229x-271y=771-729

⇒ 42 ( x − y ) = 42 ⇒ x − y = 1 \Rightarrow 42(x-y)=42 \Rightarrow x-y=1

Then evaluate x x and y y :

x + y + x − y = 3 + 1 ⇒ 2 x = 4 ⇒ x = 2 x+y+x-y=3+1 \Rightarrow 2x=4 \Rightarrow x=\boxed{\color{#D61F06}{2}}

x + y − x + y = 3 − 1 ⇒ 2 y = 2 ⇒ y = 1 x+y-x+y=3-1 \Rightarrow 2y=2 \Rightarrow y= \boxed{\color{#20A900}{1}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Denton Young
Aug 26, 2015

Add the two equations: 500x + 500y = 1500

Subtract the two equations: 46x - 46y = 46

so x + y = 3 and x - y = 1. Figure out the rest in your head :)

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Well this ques. Could have been made a little harder if options were to be removed.....as one can readily try 3 option and it is only one that is correct

Mohit Gupta - 5 years, 9 months ago

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I wasn't trying to make it difficult. It's supposed to be a level 1 question :)

Like I said, the idea is to be able to solve it in your head.

Denton Young - 5 years, 9 months ago

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