The sum of 2 numbers (x and y) is 20, and their product is 51. What are the values of x and y

Answer: 13&7

Step-by-step explanation:

The sum of two numbers x&y is 20

Product of the 2numbers xy is 51

X+y=20 ... equation 1

XY=51 ... equation 2

X=20-y ... equation 3

Substitute for x inequation 3 into equation 2

So we have;

(20-y) y=51

Open the bracket

20y-y^2=51

Collect like terms, so we have

Y2-20y+51=0

Factorise

Factors of 51 is 13&7

So - 13-7=-20 &-13*-7=51

Substitute

Y2-13y-7y+51=0

Y (y-13) - 7 (y-13) = 0

(Y-7) (y-13) = 0

Y-7=0

Y=7 or

Y-13=0

Y=13

Y=13 or 7

Substitute for y in equation 1

X+y=20

X+7=20

X=20-7

X=13 or

X+13=20

X=20-13

X=7

Therefore, X &Y = 13 &7