Final answer:
To find the product of x and y in the given system of equations, we need to solve the system and substitute the resulting values of x and y into the expression x * y. By solving the system, we find that x = 1 and y = -1. Therefore, the product of x and y is -1.
Step-by-step explanation:
To find the product of x and y, we need to solve the given system of equations.
Step 1: Multiply the first equation by 2: 2x + 2y + 2z = 4
Step 2: Add the second equation to the modified first equation: (2x + 3y - z) + (2x + 2y + 2z) = -3 + 4
Simplifying the equation, we get: 4x + 5y + z = 1
Step 3: Subtract the modified third equation from the new equation: (4x + 5y + z) - (3x + y + z) = 1 - 4
Simplifying the equation, we get: x + 4y = -3
Step 4: Solve the above equation for x: x = -3 - 4y
Step 5: Substitute the value of x in the first equation: (-3 - 4y) + y + z = 2
Simplifying the equation, we get: -3y + z = 5
Step 6: Solve the above equation for z: z = 5 + 3y
Step 7: Substitute the values of x and z in the second equation: 2(-3 - 4y) + 3y - (5 + 3y) = -3
Simplifying the equation, we get: -6 - 8y + 3y - 5 - 3y = -3
Combining like terms, we get: -8y + 3y - 3y = -3 + 6 + 5
Simplifying the equation, we get: -8y = 8
Dividing both sides by -8, we get: y = -1
Step 8: Substitute the value of y in the equation x = -3 - 4y: x = -3 - 4(-1)
Simplifying the equation, we get: x = 1
The product of x and y is: x * y = 1 * -1 = -1