To solve this system of linear equations, we can use the method of substitution or elimination.

Using substitution method:
From the second equation, we can express y in terms of x:
y = 150 - x

Now, substitute this value of y into the first equation:
0.1x + 0.15(150 - x) = 18
0.1x + 22.5 - 0.15x = 18
-0.05x + 22.5 = 18
-0.05x = -4.5
x = -4.5 / -0.05
x = 90

Now, substitute the value of x back into the second equation to find y:
90 + y = 150
y = 60

Therefore, the solution to the system of equations is x = 90 and y = 60.