Is the ordered pair (4,1) a solution to the system of equations:

Question

x+2y=6
x-y=3
Yes or no explain why

Answer 1

Yes. To check if the ordered pair (4,1) is a solution to the system of equations, substitute the values of x and y into each equation:

For the first equation:
x + 2y = 6
4 + 2(1) = 6
4 + 2 = 6
6 = 6

For the second equation:
x - y = 3
4 - 1 = 3
3 = 3

In both cases, the left side of the equation equals the right side, so the ordered pair (4,1) is a solution to the system of equations.