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Answer 1 · 2017-02-03T20:58:12

Peter is 13 and Luke is 24.

Suppose Luke is $L$ years old and Peter is $P$ years old.

Here is how you write "Luke's age is 2 less than twice Peter's age":
$L = 2P-2$

Here is how your write "The sum of their ages is 37":
$L+P=37$

We can replace $L$ with $2P-2$ in the second equation.

$color(red)L" "+P=37$
$color(red)(2P-2)+P=37$
$3P-2=37$
$3P=39$
$P=13$ . So Peter is 13 years old.

Now you can replace $P$ with $13$

$L=2*color(red)P-2$
$L=2*color(red)13-2$
$L=26-2$
$L=24$ . So Luke is 24 years old.