Answer:
11 and 5
Step-by-step explanation:
Let x and y be the two numbers
First statement says "sum of two numbers is 16", so ...
[tex]x + y = 16[/tex]
and the second statement says "sum of their squares is 146", so ...
[tex] {x}^{2} + {y}^{2} = 146[/tex]
Using substitution method
[tex]x + y = 16 \\ y = 16 - x[/tex]
Substitute the y to 2nd equation
[tex] {x}^{2} + {y}^{2} = 146 \\ {x}^{2} + {(16 - x)}^{2} = 146 \\ {x}^{2} + 256 - 32x + {x}^{2} = 146 \\ 2 {x}^{2} - 32x + (256 - 146) = 0 \\ 2 {x}^{2} - 32x + 110 = 0[/tex]
[tex]{x}^{2} - 16x + 55 = 0 \\ (x - 11)(x - 5) = 0[/tex]
In this case, if ...
[tex]x - 11 = 0 \\ x = 11[/tex]
then
[tex]y = 16 - 11 \\ y = 5[/tex]
And if
[tex]x - 5 = 0 \\ x = 5[/tex]
then ...
[tex]y = 16 - 5 \\ y = 11[/tex]
So it means the two numbers are 11 and 5
