Question 418982
Let {{{x}}} = Jack's age now
Let {{{y}}} = Jill's age now
given:
(1) {{{x - 12 = 5*(y - 12)}}}
(2) {{{y + 3 = (1/2)*(x + 3)}}}
This is 2 equations with 2 unknowns, 
so it is solvable
(1) {{{x - 12 = 5*(y - 12)}}}
(1) {{{x - 12 = 5y - 60}}}
(1) {{{ x - 5y = -48 }}}
and
(2) {{{y + 3 = (1/2)*(x + 3)}}}
(2) {{{ 2y + 6 = x + 3 }}}
(2) {{{ x - 2y = 3 }}}
Subtract (1) from (2)
(2) {{{ x - 2y = 3 }}}
(1) {{{ -x + 5y = 48 }}}
{{{3y = 51}}}
{{{ y = 17 }}}
and, since
{{{x - 2y = 3}}}
{{{x - 34 = 3}}}
{{{x =37}}}
Jack is 37 and Jill is 17
check:
(2) {{{y + 3 = (1/2)*(x + 3)}}}
(2) {{{17 + 3 = (1/2)*(37 + 3)}}}
{{{ 20 = 40/2 }}}
{{{40 = 40 }}}
OK