Question

Hey all! I'm in an acadmic competition and I'm wondering how to solve questions like these very quickly. If you could help out it would be great.

Solve for x and y below.

x+y=26

xy=165

Thanks!

Answer 1

Explanation:

The other helper has given the standard solution.

Now IF (and only if) the equations are always in the form of x+y = constant1 and xy = constant2, there is a faster way by factorizing the constant.

Note that 165 = 3*5*11

Then also note that (3*5) + 11 = 26

So you can get the two answers, 11 and 15, very quickly!

Answer 2

x=15, y=11 or x=11, y=15

Explanation:

no quick or easy way to solve sys of eqns like this:

(1) x+y=26

and

(2) xy=165

rearranging (1),

y=26-x

substituting into (2),

x(26-x)=165

expanding n rearranging,

26x-x^2=165

x^2-26x+165=0

(x-15)(x-11)=0

x-15=0 or x-11=0

x=15 or x=11

y=26-15 or y=26-11

y=11 or y=15

so x=15, y=11

or x=11, y=15