To solve the system using the method of addition, you need to manipulate the equations so that when you add them together, one variable will be eliminated.
In this case, you can multiply the first equation by 0.02 and the second equation by -2. This will make the coefficients of y in both equations equal and opposite, allowing you to eliminate the variable y when you add the equations together.
When you multiply the first equation by 0.02, you get:
0.02x - 0.02y = 20
When you multiply the second equation by -2, you get:
-0.16x - 0.04y = -620
Now, if you add these two equations together, you get:
0.02x - 0.02y + (-0.16x - 0.04y) = 20 + (-620)
Combining like terms:
-0.14x - 0.06y = -600
Therefore, the correct coefficient for x in the second equation is -0.14, not -2. To represent this correctly, the book used the number -25 as an approximation for -0.14.
(-0.14 ≈ -25 when rounded to the nearest whole number)
So, the correct system of equations is:
2x - 2y = 2000
-25x - 0.5y = -7750