Is the ordered pair (4,1) a solution to the system of equations: x+2y=6 x−y=3 Then explain your answer below. Yes Yes No No
No.
To determine if the ordered pair (4,1) is a solution to the system of equations, we substitute x = 4 and y = 1 into both equations and see if they are satisfied.
For the first equation, x + 2y = 6, we substitute x = 4 and y = 1:
4 + 2(1) = 6
4 + 2 = 6
6 = 6
This equation is satisfied, so far so good.
However, for the second equation, x - y = 3, we substitute x = 4 and y = 1:
4 - 1 = 3
3 = 3
This equation is satisfied as well.
Since the ordered pair (4,1) satisfies both equations, it is indeed a solution to the system of equations. So the answer is "Yes".