Question

Himpunan penyelesaian dari persamaan 2x + 4y = 8 untuk x € {0, 1, 2, 3, 4, 5} dan y € {bilangan bulat} adalah......

a. {(0, 8), (1, 6), (2, 4), (3, 2), (4, 0), (5, -2)}
b. {(0, 2), (2, 3), (4, 4)}
c. {(0, -2), (2, -1), (4, 0)}
d. {(0, 2), (2, 1), (4, 0)}

Answer 1

The correct solution set for the linear equation 2x + 4y = 8, given the domains for x and y, is {(0, 2), (2, 1), (4, 0)}, which is option d.

Step-by-step explanation:

To find the solution set of the equation 2x + 4y = 8 with the given domains for x and y, we can substitute each x-value into the equation and solve for the corresponding y-values. Remember that y must be an integer.

• For x = 0: 2(0) + 4y = 8 → y = 2
• For x = 1: 2(1) + 4y = 8 → y = 1.5 (not an integer, so we exclude it)
• For x = 2: 2(2) + 4y = 8 → y = 1
• For x = 3: 2(3) + 4y = 8 → y = 0.5 (not an integer, so we exclude it)
• For x = 4: 2(4) + 4y = 8 → y = 0
• For x = 5: 2(5) + 4y = 8 → y = -1 (not in the domain of y, so we exclude it)

Therefore, the correct solution set based on the given domains is {(0, 2), (2, 1), (4, 0)}, which corresponds to option d.