Answer: The correct answer is option D; (-2, 9), (4, -3)
Step-by-step explanation: The ordered pairs that can be used to graph an equation can best be explained as those values of x and y such that when plotted on the graph along the x and y axes, you would have a graphical solution for the equation. Just as a simultaneous equation helps you find the values that would satisfy your pair of equations, same way your ordered pairs would help you determine which values of x and y are correct for your equation on a graph.
To begin with, you take a value for x (since the pair is by standard written as [x, y] ). For the equation 2x + y = 5 we shall start with x equals 1 as follows;
If x = 1,
2(1) + y = 5
2 + y = 5
y = 5 - 2
y = 3 (1, 3)
If x = 2,
2(2) + y = 5
4 + y = 5
y = 5 - 4
y = 1 (2, 1)
If x = 3,
2(3) + y = 5
6 + y = 5
y = 5 - 6
y = -1 (3, -1)
If x = 4,
2(4) + y = 5
8 + y = 5
y = 5 - 8
y = -3 (4, -3)**
If x = 5,
2(5) + y = 5
10 + y = 5
y = 5 - 10
y = -5 (5, -5)
We shall now take the values from the negative side of the x axis.
If x = -1,
2(-1) + y = 5
-2 + y = 5
y = 5 + 2
y = 7 (-1, 7)
If x = -2,
2(-2) + y = 5
-4 + y = 5
y = 5 + 4
y = 9 (-2, 9)**
If x = -3,
2(-3) + y = 5
-6 + y = 5
y = 5 + 6
y = 11 (-3, 11)
If x = -4,
2(-4) + y = 5
-8 + y = 5
y = 5 + 8
y = 13 (-4, 13)
If x = -5,
2(-5) + y = 5
-10 + y = 5
y = 5 + 10
y = 15 (-5, 15)
From our calculations above, the pair that satisfies the equation from the options given in the question have been asterisked and these are;
(-2, 9), (4, -3)
