An algebra problem by I Gede Arya Raditya Parameswara

Algebra Level 3

{ 2 x + 3 y = 5 2 x 2 + 2 x y + y 2 = 5 \begin{cases} 2x+3y=5\\ 2x^{2}+2xy+y^{2}=5\end{cases}

Let x x and y y be numbers satisfying the system of equations above.

What is the sum of all possible value of y y ?


The answer is 4.

I Gede Arya Raditya Parameswara by I Gede Arya Raditya Para… , 17

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1 solution

Abhijit Dixit
Mar 4, 2017

Substitute y = 5 − 2 x 3 y= \frac{5-2x}{3} giving x = 1 , − 2 x=1,-2 and hence y = 1 , 3 y=1,3

1 Helpful 0 Interesting 0 Brilliant 0 Confused

x can also -5,-8,-11,...

I Gede Arya Raditya Parameswara - 4 years, 3 months ago

No, counter example

for -5 both equation give different values of y

ABHIJIT DIXIT - 4 years, 3 months ago

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