Question

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x + y = -8 x - y = 14

Answer 1

The system of equations is solved using the method of elimination, resulting in the solution x = 3 and y = -11, which can be expressed in set notation as {(3, -11)}.

Step-by-step explanation:

To solve the system of equations, we must find a value for x and a value for y that satisfy both equations simultaneously. We have two equations:

x + y = -8

x - y = 14

We can use the method of addition (or elimination) to find the values of the unknowns. By adding the two equations, y-terms will cancel out:

(1) x + y = -8

(2) x - y = 14

Add (1) and (2):

(1) + (2) gives 2x = 6

Dividing both sides by 2:

x = 3

Now, we can substitute the value of x into one of the original equations to solve for y. Let's use the first equation:

3 + y = -8

Subtract 3 from both sides:

y = -11

So, the solution to the system of equations is x = 3 and y = -11. In set notation, the solution set is {(3, -11)}.