How do you solve the following system?: #-x -y =2, x -y = -1#

To solve the system, we can use the method of substitution or elimination. Let's use elimination:

Given the equations:

1. -x - y = 2
2. x - y = -1

Adding equation 1 and equation 2, we get: (-x - y) + (x - y) = 2 + (-1) Simplifying: -x - y + x - y = 1 Combining like terms: -2y = 1 Divide both sides by -2: y = -1/2

Now, substitute the value of y into either equation 1 or equation 2. Let's use equation 2: x - (-1/2) = -1 Simplify: x + 1/2 = -1 Subtract 1/2 from both sides: x = -1 - 1/2 x = -3/2

So, the solution to the system is x = -3/2 and y = -1/2.

To solve the system of equations (-x - y = 2) and (x - y = -1), you can use the method of substitution or elimination.

Using substitution:

1. Solve one of the equations for one variable. For example, from the second equation, (x = y - 1).
2. Substitute the expression for the solved variable into the other equation. In this case, substitute (x = y - 1) into the first equation: (- (y - 1) - y = 2).
3. Simplify the equation and solve for the remaining variable. (y - 1 - y = 2 \Rightarrow -1 = 2), which is not true. This indicates that the system has no solution.

Using elimination:

1. Add the two equations together to eliminate one variable. ((-x - y) + (x - y) = 2 + (-1) \Rightarrow -2y = 1 \Rightarrow y = -\frac{1}{2}).
2. Substitute the value of (y) back into one of the original equations to solve for (x). Using the first equation: (-x - (-\frac{1}{2}) = 2 \Rightarrow -x + \frac{1}{2} = 2 \Rightarrow -x = \frac{3}{2} \Rightarrow x = -\frac{3}{2}).

So, the solution to the system is (x = -\frac{3}{2}) and (y = -\frac{1}{2}).