Answer: To find which point is a solution to a system of linear equations, you need to substitute the x and y values of each point into both equations and check if the results are true for both equations. If the results are true, then the point is a solution.
For the first point, (6, -1):
Substituting x = 6 and y = -1 into the first equation:
y = -x + 5
-1 = -6 + 5
-1 = -1 (true)
Substituting x = 6 and y = -1 into the second equation:
x - 3y = 9
6 - 3(-1) = 9
6 + 3 = 9
9 = 9 (true)
Since both equations are true, (6, -1) is a solution to the system of linear equations.
For the second point, (4, 1):
Substituting x = 4 and y = 1 into the first equation:
y = -x + 5
1 = -4 + 5
1 = 1 (true)
Substituting x = 4 and y = 1 into the second equation:
x - 3y = 9
4 - 3(1) = 9
4 - 3 = 9
1 = 9 (false)
Since the second equation is false, (4, 1) is not a solution to the system of linear equations.
Similarly, you can check the other points and find that the only solution to the system of linear equations is (6, -1).
Explanation: