To solve the given system of equations using the comparison method, we will compare the coefficients of either x or y in both equations. Let's solve the system step by step.

Given equations:
1) 0.5x - 0.3y = 4.56
2) 0.02x - 0.9y = -0.912

Step 1: Choose a variable to eliminate
In this case, we will eliminate the variable x. To do this, we need to multiply both equations by appropriate coefficients such that the coefficients of x in both equations become equal or opposite.

Step 2: Multiply the equations by appropriate coefficients
Let's multiply equation 1 by 100 to eliminate the decimal points:
1) 100 * (0.5x - 0.3y) = 100 * 4.56
50x - 30y = 456

Now, let's multiply equation 2 by 5 to eliminate the decimal points:
2) 5 * (0.02x - 0.9y) = 5 * (-0.912)
0.1x - 4.5y = -4.56

Step 3: Compare the coefficients of x
Now, we can compare the coefficients of x in both equations:
50x - 30y = 456
0.1x - 4.5y = -4.56

The coefficients of x in both equations are 50 and 0.1, respectively. To eliminate x, we need the coefficients to be equal but opposite in sign.

Step 4: Multiply the equations to make coefficients of x opposite
To make the coefficients of x opposite, we can multiply equation 2 by -500:
2) -500 * (0.1x - 4.5y) = -500 * (-4.56)
-50x + 2250y = 2280

Now, we have the following system of equations:
50x - 30y = 456
-50x + 2250y = 2280

Step 5: Add the equations to eliminate x
Now, we can add the equations together:
(50x - 30y) + (-50x + 2250y) = 456 + 2280
2220y = 2736

Step 6: Solve for y
Divide both sides of the equation by 2220:
y = 2736 / 2220
y = 1.23

Step 7: Substitute the value of y into one of the original equations
Let's substitute y = 1.23 into equation 1:
0.5x - 0.3(1.23) = 4.56
0.5x - 0.369 = 4.56
0.5x = 4.56 + 0.369
0.5x = 4.929
x = 4.929 / 0.5
x = 9.858

Step 8: Check the solution
Substitute the values of x and y into the second equation:
0.02(9.858) - 0.9(1.23) = -0.912
0.19716 - 1.107 = -0.912
-0.