The amount of interest earned each year on amount x would be 10% of x or 0.1x   

The amount of interest earned each year on amount y would be 6% of y or 0.06y 

The total interest is $18,000 so 0.1x + 0.06y = 18,000 

The total invested is $200,000 so x + y = $200,000 

So buy subtracting x from both sides of this equation you have y = 200,000 - x

So you can substitute 200,000 - x in the place of y in the first equation 

0.1x + 0.06(200,000 - x) = 18,000    Now we mulitply to eliminate the ( ). 

0.1x + 12,000 - 0.06x = 18,000  which simplifies to 0.04x + 12,000 = 18,000

Subtracting 12,000 from both sides of the equation shows that 0.04x = 6,000

When we divide 6,000 by 0.04 to get x alone, we find that x = $150,000.

$200,000 - $150,000 = $50,000 = y    So $150,000 was invested at 10% and $50,000 was invested at 6%