Choice D) x*y = -10
Explanation:
Multiply both sides of the first equation by 10 to clear out the fractions (10 is the LCD)
3x/5 + y/2 = 13/10
10*(3x/5 + y/2) = 10*(13/10)
6x + 5y = 13
Multiply both sides of the second equation by 100 to get each decimal value to turn into a whole number (move the decimal point over 2 spots to the right)
0.5y + 0.04x = 2.42
50y + 4x = 242
4x + 50y = 242
So we have this new system of equations which is equivalent to the original system
6x + 5y = 13
4x + 50y = 242
Multiply both sides of the top equation by 10 so that the 5y turns into 50y
6x + 5y = 13
10*(6x + 5y) = 10*13
60x + 50y = 130
Now we have this system of equations
60x + 50y = 130
4x + 50y = 242
If we subtract straight down then we have
60x-4x = 56x
50y-50y = 0y = 0 ... notice how the y terms go away effectively
130-242 = -112
The y terms go away leaving us with this simplified equation
56x = -112
Which solves to
x = -2
when we divide both sides by 56
Now use that x value to find y
6x + 5y = 13
6(-2) + 5y = 13 ... replace x with -2
-12 + 5y = 13
-12+5y+12 = 13+12 ... adding 12 to both sides
5y = 25
5y/5 = 25/5 dividing both sides by 5
y = 5
In summary we have x = -2 and y = 5. Therefore, x*y = -2*5 = -10 is the answer
