The product of two numbers is 26 and one of the numbers is one larger than six times the other number. find the numbers.

(-13/6, -12)

&

(2, 13)

Step-by-step explanation:

x · y = 26       > x = 26/y

y = 1 + 6x

SUB for y

x(1 + 6x) = 26

x + 6x² = 26

SOLVE for x

6x² + x - 26 = 0

6x² + 13x - 12x - 26 = 0

6x(x - 2) 13(x - 2) = 0

(6x + 13)(x - 2) = 0

x = -13/6 or 2

Test x = -13/6 for both equations

Equation 1

-13/6 · y = 26

y = -156/13

y = -12

Equation 2

y = 1 + 6(-13/6)

y = 1 - 13

y = -12

-12 = -12 ✅

Test x = 2 for both equations

Equation 1

2 · y = 26

y = 26/2

y = 13

Equation 2

y = 1 + 6(2)

y = 1 + 12

y = 13

13 = 13 ✅

Hope this helps & God bless!