Question 12

B) (0,2) is not a solution to the equation x - 2y = 4.

To determine which option does not satisfy the equation x - 2y = 4, we can substitute the coordinates of each option into the equation. When we substitute (0, 2) into the equation, we find that it does not hold true.

A) (-2,-3)

Substituting (-2, -3) into the equation gives us -2 - 2(-3) = -2 + 6 = 4, which satisfies the equation. Therefore, this point is a solution.

B) (0,2)

Substituting (0, 2) into the equation results in 0 - 2(2) = 0 - 4 = -4, which does not equal 4. Therefore, this point is not a solution to the equation.

C) (4,0)

Substituting (4, 0) into the equation results in 4 - 2(0) = 4 - 0 = 4, which satisfies the equation. Thus, this point is a solution.

D) (8,2)

Substituting (8, 2) into the equation results in 8 - 2(2) = 8 - 4 = 4, which satisfies the equation. Therefore, this point is also a solution.

Conclusion

The point (0, 2) does not satisfy the equation x - 2y = 4, making it the only option that does not fit. In contrast, the other options all successfully meet the criteria of the equation, confirming that they are valid solutions. Thus, (0, 2) is definitively the correct answer.