Solve the following systems of equations using the addition (elimination) method.
What type of system is it? Name the solution if there is one.
13. x+y=6
x-y=4
To solve the system of equations using the addition (elimination) method, we'll add the two equations together to eliminate one of the variables.
Adding the two equations:
(x + y) + (x - y) = 6 + 4
Simplifying:
2x = 10
Dividing both sides by 2:
x = 5
Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
5 + y = 6
Subtracting 5 from both sides:
y = 1
Therefore, the solution to this system of equations is x = 5 and y = 1.
Now, let's identify the type of system. This system is called a consistent system because it has a unique solution. The solution to this system is (5, 1).
x+y=6
x-y=4 -
2y=2
y=1
x=5