Dare you to use substitution

Algebra Level 3

Given the following simultaneous equations x + 6 y = 25 \sqrt{x} + 6\sqrt{y} = 25 2 y 4 − 3 x = 5 2y^{4} - 3x = 5 find the value of x + y x + y .


The answer is 173.

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Yuxuan Seah by Yuxuan Seah , 20, Singapore

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3 solutions

Vraj Mistry
May 23, 2015

Was just too easy but took almost 11 min. Only substitute values for y which are perfect squares and find value of x; I got y=4 , x=169

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ripin Yadav
Jan 5, 2015

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Dileeban R K
Aug 17, 2014

If x=169,y=4 substitute in the given equation

0 Helpful 0 Interesting 0 Brilliant 0 Confused

How did you get this????

Sanjana Nedunchezian - 6 years, 9 months ago

I suppose it's trying to make an educated guess and hope for the best. Looking at the second equation, if y increases, then so does x. When y = 1, the values of x and y are not big enough to fulfill the 1st equation. So we keep trying successively larger values of y. And we get lucky!

Kenneth Tay - 6 years, 9 months ago

@Yuxuan Seah - what happened to your streak? :o

Astro Enthusiast - 6 years, 8 months ago

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Sigh...I guess I was too careless... @Astro Enthusiast

Yuxuan Seah - 6 years, 8 months ago

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