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

Question

x+2y=6
x-y=3

then explain your answer below.

yes
no

Answer 1

No, the ordered pair (4,1) is not a solution to the system of equations.

To determine if an ordered pair is a solution to a system of equations, we substitute the values of x and y into each equation and see if both equations are true.

Let's substitute x=4 and y=1 into the first equation:

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

This equation is true.

Now let's substitute x=4 and y=1 into the second equation:

4 - 1 = 3
3 = 3

This equation is also true.

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