Question 610698
Let x and y be the two numbers


The product of two numbers is 84.
xy=84.........(1)
One number is 13 more than 2 times the other.
x=2y+13..............(2)
Substitute the value of x in (1)
(2y+13)y=84
2y^2+13y=84
2y^2+13y-84=0
Solve for y
*[invoke quadratic "y", 2, 13, -84 ]
So
y=4 or y=-10.5(inadmissible) 
Put the value of y=4 in (1)
xy=84
4x=84
x=84/4
x=21

x,y = 21,4


Check
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xy=84
21*4=84
84=84


x=2y+13
21=2(4)+13
21=8+13
21=21