Question

3x - y = 8 - x ,6x + 4y = 2y-9 For the system of equations above, what is the value of the product xy?

(A) -3
(B) -2
(C) 2
(D) 3

Answer 1

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:

1. Start by adding x to both sides of the first equation to isolate the x term: 3x + x - y = 8.
2. Simplify the equation to 4x - y = 8.
3. Next, multiply the second equation by 4 to eliminate the y term: 24x + 16y = 8y - 36.
4. Simplify the equation to 24x - 8y = -36.
5. Now, you have a system of two equations with two variables: 4x - y = 8 and 24x - 8y = -36.
6. Multiply both sides of the first equation by 8 to get 32x - 8y = 64.
7. Subtract the second equation from the modified first equation: 32x - 8y - (24x - 8y) = 64 - (-36).
8. Simplify the equation to get 8x = 100.
9. Divide both sides by 8 to solve for x: x = 12.5.
10. 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.
11. Simplify the equation to get 37.5 - y = 8.
12. Subtract 37.5 from both sides to isolate the y term: -y = 8 - 37.5.
13. Simplify the equation to -y = -29.5.
14. 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.