Final answer:
From the given options for ordered pairs, only (0, 4) and (-2, 8) are solutions to the equation 2x + y = 4. Each pair is substituted into the equation to verify if it satisfies the equation.
Step-by-step explanation:
The subject of this question is to find out which ordered pairs are solutions to the given linear equation 2x + y = 4. To determine if an ordered pair (x, y) is a solution, you substitute the x- and y-values into the equation and see if the equation holds true.
For the ordered pair (0, 4), substituting x = 0 and y = 4 gives 2(0) + 4 = 4, which is true. So, (0, 4) is a solution.
For the ordered pair (4, 0), substituting x = 4 and y = 0 gives 2(4) + 0 = 8, which is not equal to 4. So, (4, 0) is not a solution.
The ordered pair (1,3) is not listed correctly in the question. If this was meant to be (1, 3), it also does not satisfy the equation, as 2(1) + 3 = 5, not 4.
For the ordered pair (-2, 8), substituting x = -2 and y = 8 gives 2(-2) + 8 = 4, which is true. So, (-2, 8) is a solution.
The ordered pair (8, -2) is written as (8.-2), assuming the dot is a typo and should be a comma. Using x = 8 and y = -2 gives 2(8) - 2 = 16 - 2 = 14, which does not equal 4. Therefore, (8, -2) is not a solution.
Finally, for the ordered pair (3/2, -1), substituting x = 3/2 and y = -1 we get 2(3/2) - 1 = 3 - 1 = 2, which is not equal to 4. So, (3/2, -1) is not a solution.
The correct solutions to the equation from the given pairs are (0, 4) and (-2, 8).