Question 494836
your equations are:


7r - 3s = 33 (first equation)
3r + 7s = 39 (second equation)


multiply first equation by 3 to get:
21r - 9s = 99 (third equation)


multiply second equation by 7 to get:
21r + 49s = 273 (fourth equation.


your equations are now:


21r - 9s = 99 (third equation)
21r + 49s = 273 (fourth equation)


subtract third equation from fourth equation to get:


58s = 174
divide both sides of this equation by 58 to get:
s = 3


substitute for s in the first equation to get:
7r - 3s = 33 (first equation) becomes:
7r - 9 = 33 
add 9 to both sides of this equation to get:
7r = 42
divide both sides of this equation by 7 to get:
r = 6


you have:
r = 6
s = 3


substitute for r and s in the second equation to get:


3r + 7s = 39 (second equation) becomes:
18 + 21 = 39 
combine like terms to get:
39 = 39


this confirms that the values for r and s are good.


the answer to this problem is:
r = 6
s = 3