Question

How many solutions does the system of linear equations below have?

-x - y = 3
2x + 2y = 4
A. One
B. None
C. Infinitely many
D. Two

Answer 1

Upon simplifying and comparing the two given linear equations, it becomes clear that the system has no solutions since the equations represent two parallel lines that never intersect.

Step-by-step explanation:

To determine how many solutions the system of linear equations has, we need to analyze the equations:

• -x - y = 3
• 2x + 2y = 4

First, we can simplify the second equation by dividing everything by 2, which gives us:

• x + y = 2

Now, let's multiply the first equation by -1 to get:

• x + y = -3

When we compare the two new equations, we see that they have the same left-hand side, but the right-hand sides are different constants (2 and -3). This means that the system of equations has no solutions, as the two lines are parallel and do not intersect. Therefore, the correct answer is:

• B. None