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
