GATE 2017 EE (EE2) – Question 29

Engineering Mathematics · Linear Algebra: Systems of linear equations · 1 mark · Numerical answer

Integers x,y satisfy $2x^2+y^2=34$ and $x+2y=11$. The value of x+y is ________.

Show answer and explanation

Correct answer: 7 to 7

Explanation

Substitute x=11−2y into the quadratic equation. This gives $9y^2-88y+208=0$, whose roots are y=4 and y=52/9.

The integer requirement selects y=4, so x=11−8=3. Check: 2(9)+16=34. Therefore **x+y=7**.

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