Expert: Scott A Wilson - 3/30/2011

Question
17x-6y=403
2x+9y=193

Please help me with the steps

Answer
Take 2/3 times the 2nd equation and add it to the 1st equation to get rid of y.
This gives (17 + 4/3)x +(-6+6)y = 403 + 2*193/3.

For x, since 17 = 51/3, 17 + 4/3 = (51+4)/3 = 55/3.
For y, note that -6+6 = 0.
For the right side, note that 403 = 1209/3 and 2*193/3 = 386/3, and the sum of these is 1595/3.

That gives us 55x/3 = 1595/3, so 55x = 1595.
Dividing by 5 gives 11x = 319.
Dividing by 11 gives x = 29.

Since there is a 2x in the second equation, 2*29 = 58.
That means that 58 + 9y = 193.
Subtracting 58 from both sides gives 9y = 135, so y = 15.