Given that 9x²-64y²=185 and 3x-8y=5, find the product of x and y

Answer 1

To solve this system of equations, we can use the method of substitution.

First, we solve the second equation for x:

3x - 8y = 5
3x = 8y + 5
x = (8y + 5)/3

Next, substitute x into the first equation:

9((8y + 5)/3)² - 64y² = 185
9(64y² + 80y + 25)/9 - 64y² = 185
64y² + 80y + 25 - 64y² = 185
80y + 25 = 185
80y = 160
y = 2

Now, substitute y back into the equation x = (8y + 5)/3:

x = (8(2) + 5)/3
x = (16 + 5)/3
x = 21/3
x = 7

Therefore, the product of x and y is:

x * y = 7 * 2 = 14