The sum of two numbers is zero. when 14 times the smaller number is added to 9 times the larger, the result is 1. find the two numbers.

Let's solve this problem step-by-step.

STEP-BY-STEP EXPLANATION:

We will be using simultaneous equations to solve this problem.

Let's first establish the two equations we will be using.

Let x = smaller number

Let y = larger number

Equation No. 1 -

x + y = 0

Equation No. 2 -

14x + 9y = 1

To begin with, we will make ( x ) the subject in the first equation.

Equation No. 1 -

x + y = 0

x = 0 - y

x = - y

Next we will substitute the value of ( x ) from the first equation into the second equation to solve for ( y ).

Equation No. 2 -

14x + 9y = 1

14 ( - y ) + 9y = 1

- 14y + 9y = 1

- 5y = 1

y = 1 / - 5

y = - 1 / 5

Then we will substitute the value of ( y ) from the second equation into the first equation to solve for ( x ).

Equation No. 1 -

x = - y

x = - ( - 1 / 5 )

x = 1 / 5

FINAL ANSWER:

Therefore, the two numbers 1 / 5 and - 1 / 5.

Hope this helps! :)
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