Is the ordered pair (4,1) a solution to the system of equations: x+2y=6 x−y=3 Then explain your answer below.
We can check if the ordered pair (4,1) is a solution to the system of equations by substituting the values of x and y into each equation:
For the first equation, x + 2y = 6, substitute x = 4 and y = 1:
4 + 2(1) = 6
4 + 2 = 6
6 = 6
Since the equation is true, (4,1) satisfies the first equation.
For the second equation, x - y = 3, substitute x = 4 and y = 1:
4 - 1 = 3
3 = 3
Again, the equation is true, so (4,1) satisfies the second equation.
Since (4,1) satisfies both equations in the system, it is a solution to the system of equations.