Answer:
Explanation:
To determine which of the given ordered pairs represents the solution to the system of equations, we can substitute the values of x and y into the equations and check if they satisfy both equations.
The system of equations is:
Equation 1: x - 4y = 7
Equation 2: 5x + 9y = 6
Let's check each ordered pair:
(3, -1)
Substituting x = 3 and y = -1 into the equations:
Equation 1: 3 - 4(-1) = 7
3 + 4 = 7
7 = 7 (True)
Equation 2: 5(3) + 9(-1) = 6
15 - 9 = 6
6 = 6 (True)
Since both equations are satisfied, (3, -1) is a solution to the system.
(3, 1)
Substituting x = 3 and y = 1 into the equations:
Equation 1: 3 - 4(1) = 7
3 - 4 = 7
-1 = 7 (False)
Equation 2: 5(3) + 9(1) = 6
15 + 9 = 6
24 = 6 (False)
Since one or both equations are not satisfied, (3, 1) is not a solution to the system.
(1, -3)
Substituting x = 1 and y = -3 into the equations:
Equation 1: 1 - 4(-3) = 7
1 + 12 = 7
13 = 7 (False)
Equation 2: 5(1) + 9(-3) = 6
5 - 27 = 6
-22 = 6 (False)
Since one or both equations are not satisfied, (1, -3) is not a solution to the system.
(-1, -3)
Substituting x = -1 and y = -3 into the equations:
Equation 1: -1 - 4(-3) = 7
-1 + 12 = 7
11 = 7 (False)
Equation 2: 5(-1) + 9(-3) = 6
-5 - 27 = 6
-32 = 6 (False)
Since one or both equations are not satisfied, (-1, -3) is not a solution to the system.
Therefore, the ordered pair (3, -1) represents the solution to the system of equations.