Question 408274
Call the numbers {{{a}}} and {{{b}}}
given:
(1) {{{a + b = 17}}}
(2) {{{6a = 2b - 2}}} (assume {{{a}}} is the smaller)
This is 2 equations with 2 unknowns, so when 
number of equations = number of unknowns,
the system is solvable
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Subtract {{{2b}}} from both sides of (2)
(2) {{{6a - 2b = -2}}}
Multiply both sides of (1) by {{{2}}}, and
add (1) and (2)
(1) {{{2a + 2b = 34}}}
(2) {{{6a - 2b = -2}}}
{{{8a = 32}}}
{{{a = 4}}}
and, from (1),
(1) {{{a + b = 17}}}
{{{4 + b = 17}}}
{{{b = 13}}}
The larger is 13 and the smaller is 4
check answer:"
(2) {{{6a = 2b - 2}}}
(2) {{{6*4 = 2*13 - 2}}}
{{{24 = 26 - 2}}}
{{{24 = 24}}}
OK