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Answer: Distance from the point (x, y) to the origin is approximately 11 units.
Step-by-step explanation: Given equations x+y=13 and xy =24.
Solving first equation for y, we get
y = 13-x.
Substituting y=13-x in second equation, we get
x(13-x)= 24.
13x -x^2=24.
-x^2+13x =24.
-x^2+13x -24=0.
Dividing each term by -1, we get
x^2-13x+24=0.
Applying quadratic formula
Plugging x=10.77 in first equation
y= 13-10.77 = 2.23
and plugging x=2.23 in first equation, we get
y = 13-2.23 = 10.77.
Therefore, (x,y) are (10.77, 2.23) and (2.23, 10.77).
Now, we need to find the distance of (x,y) from origin (0,0).
Applying distance formula :