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To solve this system of equations, we can use the method of substitution.
1) 10x - 2y = 18
2) -10x + 9y = -46
From equation 2), we can solve for x:
-10x = -46 - 9y
x = (46 + 9y)/10
Now, substitute this value of x into equation 1):
10((46 + 9y)/10) - 2y = 18
46 + 9y - 2y = 18
7y + 46 = 18
7y = -28
y = -4
Substitute the value of y back into the x expression:
x = (46 + 9(-4))/10
x = (46 - 36)/10
x = 10/10
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -4.