Question

X+y=

−1
x−y=
−5
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The system has a single solution. The solution set is enter your response here.
​(Type an ordered pair. Type integers or simplified​ fractions.)
B.
There are infinitely many solutions and the equations are dependent. The solution set is {(x,y) 2x+y=−1}.
C.
The system is inconsistent. The solution set is the empty set.

Answer 1

A. The system has a single solution. The solution set is (x, y) = (-3, 2).

Explanation:

You want the solution to the system of equations ...

• x + y = -1
• x - y = -5

Number of solutions

These standard form equations are different, so they will have one solution.

Solution

That solution can be found by adding the equations, eliminating the y-variable.

(x +y) +(x -y) = (-1) +(-5)

2x = -6

x = -3

y = x +5 = -3 +5 = 2 . . . . . . from the second equation

The solution is (x, y) = (-3, 2).