Final answer:
To find the value of the product xy in the given system of equations, solve for x and y and multiply their values together.
Step-by-step explanation:
To solve the given system of equations:
- Start by adding x to both sides of the first equation to isolate the x term: 3x + x - y = 8.
- Simplify the equation to 4x - y = 8.
- Next, multiply the second equation by 4 to eliminate the y term: 24x + 16y = 8y - 36.
- Simplify the equation to 24x - 8y = -36.
- Now, you have a system of two equations with two variables: 4x - y = 8 and 24x - 8y = -36.
- Multiply both sides of the first equation by 8 to get 32x - 8y = 64.
- Subtract the second equation from the modified first equation: 32x - 8y - (24x - 8y) = 64 - (-36).
- Simplify the equation to get 8x = 100.
- Divide both sides by 8 to solve for x: x = 12.5.
- Substitute the value of x back into one of the original equations to solve for y. Using the first equation, we have: 3(12.5) - y = 8.
- Simplify the equation to get 37.5 - y = 8.
- Subtract 37.5 from both sides to isolate the y term: -y = 8 - 37.5.
- Simplify the equation to -y = -29.5.
- Multiply both sides by -1 to solve for y: y = 29.5.
The values of x and y are x = 12.5 and y = 29.5, respectively. To find the value of the product xy, simply multiply the values of x and y together: xy = 12.5 * 29.5 = 368.75. Therefore, the value of the product xy is 368.75.