Question

the sum of two numbers is zero. when 15 times the smaller numbers is added to 10 times the larger, the result is 1. find the two numbers.

Answer 1

We have two numbers say a, b. And a system of equations.

$a+b=0\wedge\dfrac{a+b}{15}+10(a+b)=1$

It looks a bit intimidating but it's actually very easy.

Instead of term a + b in the second equation we can say it's zero because the first equation describes a + b as being equal to 0.

So,

$\dfrac{0}{15}+10\cdot0=1\Longrightarrow 0+0=1$

The above equation is not true therefore numbers a and b do not exists in the real number domain.

$a,b\notin\mathbb{R}$

No solution.

Hope this helps.