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

x+2y=6

x−y=3

1 answer

To check whether 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 see if both equations are true.

Substituting x=4 and y=1 into the first equation, we get:

4 + 2(1) = 6
4 + 2 = 6
6 = 6

Since both sides of the equation are equal, the first equation is true when x=4 and y=1.

Substituting x=4 and y=1 into the second equation, we get:

4 - 1 = 3
3 = 3

Again, both sides of the equation are equal, so the second equation is true when x=4 and y=1.

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