Is the ordered pair (4,1)

Question

a solution to the system of equations:

x+2y=6


x−y=3

Answer 1

To determine if the ordered pair (4,1) is a solution to the system of equations, we substitute the values of x and y into each equation and check if both equations are true:

For the first equation:
x + 2y = 6
Substituting x = 4 and y = 1:
4 + 2(1) = 6
4 + 2 = 6
6 = 6
The first equation is true.

For the second equation:
x - y = 3
Substituting x = 4 and y = 1:
4 - 1 = 3
3 = 3
The second equation is true.

Since both equations are true when substituting x = 4 and y = 1, the ordered pair (4,1) is indeed a solution to the system of equations.