Question

sum of the two number is 19 and the greater number exceeds twice the smaller by 14 find the numbers​

Answer 1

Let the two numbers be x and y.

In this y is the greater number and x is the smaller number.

Now,

First case states :-

$x + y = 19$

Next case states :-

$y = 2x + 14$

Now,

Solving the two equations :-

$x + y = 19 \\ \\ \\x + 2x + 14 = 19 \\ \\ \\3x = 19 - 14 \\ \\ \\3x = 5 \\ \\ \\x = \frac{5}{3} \\ \\ \\ \\ \\y = 2x + 14 \\ \\y = 2 \times \frac{5}{3} + 14 \\ \\ \\y = \frac{10 + 42}{3} \\ \\ \\y = \frac{52}{3}$

Therefore :-

The two numbers are 5/3 and 52/3

Answer!

Answer 2

Let greater Number Be =x

Let Smaller Number be=y

Sum of 2 number=19

X+Y=19

X=19-Y. (Equation 1)

According to Statement Given Above

Greater Number(x) Exceeds or Increase Twice the Smaller Number(y) by 14.

Means When We multiply 2 with Smaller Number and add 14 to Smaller Number it become=Greater Number

Equation Can Be Set

2Y+14=X

Putting Equation 1 on Value of x

X=2y+14

19-Y=2y+14

-y-2y=14-19

-3y=-5

y=5/3

y=5/3

X=19-Y

X=19-5/3

X=57-5/3

X=52/3

$\boxed{\mathbf{Numbers\:are=\frac{5}{3},\frac{52}{3}}}}$