Let x and y be the two numbers. 1) x + y = 19

2) xy = 78

Solve (1) for y. Subtract x from both sides.

y = 19 - x

Then we can write equation (2) as x(19-x)=78

Simplifying

x(19 + -1x) = 78

(19 * x + -1x * x) = 78

(19x + -1x2) = 78

Solving

19x + -1x2 = 78

Solving for variable 'x'.

Reorder the terms:

-78 + 19x + -1x2 = 78 + -78

Combine like terms: 78 + -78 = 0

-78 + 19x + -1x2 = 0

Factor a trinomial.

(-13 + x)(6 + -1x) = 0

==

Set the factor '(-13 + x)' equal to zero and attempt to
solve:

Simplifying

-13 + x = 0

Solving

-13 + x = 0

Move all terms containing x to the left, all other terms to the
right.

Add '13' to each side of the equation.

-13 + 13 + x = 0 + 13

Combine like terms: -13 + 13 = 0

0 + x = 0 + 13

x = 0 + 13

Combine like terms: 0 + 13 = 13

x = 13

Simplifying

x = 13

==

Set the factor '(6 + -1x)' equal to zero and attempt to
solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the
right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

==

x = {13, 6} The answer to your question is that the larger
number is 13.