Question 970302
The sum of their age is 19.


This means that when you add their ages together, it will be 19.
{{{L + R = 19}}}


The positive difference of their age is 9.



It tells you that Lily is the older child. 
Since the difference is a positive number, that means it would be Lily's age minus Rosie's age since Lily is older.
{{{L - R = 9}}}

Now you have 2 equations that can be used to find their ages.


Start with the first equation
{{{L+R=19}}}
solve for L
{{{L+R=19}}}
{{{L+R-R=19-R}}}
{{{L=19-R}}}
Now use the substitution method (replacing or "substituting" L with 19-R) for the next equation.
{{{L-R=9}}}
{{{(19-R)-R=9}}}
{{{19-2R=9}}}
{{{19-19-2R=9-19}}}
{{{-2R=-10}}}
{{{(-2)R/-2 = (-10)/-2}}}
{{{R=5}}}
Rosie's age is 5. Now use the first equation to find Lily's age.
{{{L+R=19}}}
{{{L+5=19}}}
{{{L+5-5=19-5}}}
{{{L=14}}}
Lily's age is 14.



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