Question 110139
It looks like you got half of it right:
This same problem came up a few weeks ago, this is what I submitted then
Perhaps it will help you.

Find values for m and b in the following system so that the solution to the system is (-3,4)
 
They want you find both equations of a two-equation system
 
Find the 1st equation:
5x + 7y = b
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Find b by using x,y coordinates given -3, 4
5(-3) + 7(4) = b
-15 + 28 = b
b = + 13
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Find the slope (m): using y = mx + 13, using the given coordinates again
y = mx + b
4 = m(-3) + 13
4 = -3m + 13
3m = 13 - 4
3m = 9
m = +3
:
the 1st equation: y = 3x + 13; (m = +3 and b = +13)
:
: 
Find the 2nd equation:
mx + y = 22
Find the slope (m) using the given coordinates x,y; -3,4
m(-3) + 4 = 22
-3m = 22 - 4
-3m = 18
m = 18/-3
m = -6
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Find b in the 2nd equation, using the given coordinates for x & y again
y = mx + b
4 = -6(-3) + b
4 = 18 + b
4 -18 = b
b = -14
:
The 2nd equation: y = -6x - 14; (m =- 6 and b = -14)
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If you graphed these two equations, you would find that they intersect at the given coordinates of -3,4
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