Question 699423
Let {{{ d }}} = number of dimes she has
Let {{{ q }}} = number of quarters she has
given:
(1) {{{ d + q = 30 }}}
(2) {{{ 10d + 25q = 600 }}} ( in cents )
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Using substitution, 
(1) {{{ q = 30 - d }}}
(2) {{{ 10d + 25*( 30 - d ) = 600 }}}
(2) {{{ 10d + 750 - 25d = 600 }}}
(2) {{{ -15d = -150 }}}
(2) {{{ d = 10 }}}
and
(1) {{{ d + q = 30 }}}
(1) {{{ 10 + q = 30 }}}
(1) {{{ q = 20 }}}
She has 10 dimes and 20 quarters
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You can do it by elimination, too
Multiply both sides of (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 10d + 25q = 600 }}} 
(1) {{{ -10d - 10q = -300 }}}
{{{ 15q = 300 }}}
{{{ q = 20 }}}
{{{ d = 10 }}}
OK