Question

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

x + 2y = 6
x- y = 3

Answer 1

To determine if (4,1) is a solution to the system of equations, we can substitute the values of x and y into each equation and see if they are true.

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

Since the equation is true when x = 4 and y = 1, (4,1) is a solution to the first equation.

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

Since the equation is true when x = 4 and y = 1, (4,1) is a solution to the second equation as well.

Since (4,1) is a solution to both equations, it is a solution to the system of equations.