Question 184486
Let the price of oranges be {{{a}}}
Let the price of lemons be {{{b}}}
given:
(1) {{{3a + 5b = 1026}}} (in cents)
(2) {{{6a + 4b = 1116}}} (in cents)
First, I will multiply both sides of (1) by {{{4}}}
and both sides of (2) by {{{5}}}
(1) {{{12a + 20b = 4104}}} 
(2) {{{30a + 20b = 5580}}}
Now subtract (1) from (2)
(2) {{{30a + 20b = 5580}}}
(1) {{{-12a - 20b = -4104}}} 
(3) {{{18a = 1476}}}
(3) {{{a = 82}}}
Now plug this back into either equation to find {{{b}}}
(1) {{{3a + 5b = 1026}}}
(1) {{{3*82 + 5b = 1026}}}
(1) {{{246 + 5b = 1026}}}
(1) {{{5b = 780}}}
(1) {{{b = 156}}}
The price of oranges is 82 cents each. Thw price of
lemons is $1.56 each
check answers:
(1) {{{3a + 5b = 1026}}} 
(1) {{{3*82 + 5*156 = 1026}}}
(1) {{{246 + 780 = 1026}}}
(1) {{{1026 = 1026}}} 
(2) {{{6a + 4b = 1116}}}
(2) {{{6*82 + 4*156 = 1116}}}
(2) {{{492 + 624 = 1116}}}
(2) {{{1116 = 1116}}}
OK