Question 230685
Let {{{a}}} = miles of hwy driving
Let {{{b}}} = miles of city driving
given:
Total gas used = 28 gallons 
(1) {{{a/25.7 + b/13.4 = 28}}}
(2) {{{a + b = 522.8}}}
This is 2 equations with 2 unknowns, so
it's solvable
(1) {{{a/25.7 + b/13.4 = 28}}}
Multiply both sides by {{{25.7*13.4 = 344.38}}}
(1) {{{13.4a + 25.7b = 28*344.38}}}
(1) {{{13.4a + 25.7b = 9642.64}}}
Multiply both sides of (2) by {{{13.4}}}
and subtract from (1)
(1) {{{13.4a + 25.7b = 9642.64}}}
(2) {{{-13.4a - 13.4b = -7005.52}}}
{{{12.3b = 2637.12}}}
{{{b = 214.4}}}
214.4 gallons were used for city driving
check answer:
{{{a + b = 522.8}}}
{{{a + 214.4 = 522.8}}}
{{{a = 522.8 - 214.4}}}
{{{a = 308.4}}}
and
{{{a/25.7 + b/13.4 = 28}}}
{{{308.4/25.7 + 214.4/13.4 = 28}}}
{{{12 + 16 = 28}}}
{{{28 = 28}}}
OK