To solve the system of equations:
[tex]\[
\left\{
\begin{array}{l}
2x + y = -4 \\
x - y = 4
\end{array}
\right.
\][/tex]
we will follow a detailed, step-by-step approach.
### Step 1: Write down the equations
We have the following two equations:
1. [tex]\( 2x + y = -4 \)[/tex]
2. [tex]\( x - y = 4 \)[/tex]
### Step 2: Solve one equation for one variable
Let's solve the second equation for [tex]\( x \)[/tex]:
[tex]\[ x - y = 4 \][/tex]
Adding [tex]\( y \)[/tex] to both sides, we get:
[tex]\[ x = 4 + y \][/tex]
### Step 3: Substitute the expression from Step 2 into the first equation
Now, substitute [tex]\( x = 4 + y \)[/tex] into the first equation [tex]\( 2x + y = -4 \)[/tex]:
[tex]\[ 2(4 + y) + y = -4 \][/tex]
### Step 4: Solve for [tex]\( y \)[/tex]
Expand and combine like terms:
[tex]\[ 8 + 2y + y = -4 \][/tex]
[tex]\[ 8 + 3y = -4 \][/tex]
Subtract 8 from both sides:
[tex]\[ 3y = -4 - 8 \][/tex]
[tex]\[ 3y = -12 \][/tex]
Divide by 3:
[tex]\[ y = -4 \][/tex]
### Step 5: Substitute [tex]\( y \)[/tex] back into the expression for [tex]\( x \)[/tex]
Using the expression [tex]\( x = 4 + y \)[/tex]:
[tex]\[ x = 4 + (-4) \][/tex]
[tex]\[ x = 0 \][/tex]
### Conclusion
Therefore, the solution to the system of equations is:
[tex]\[ x = 0 \][/tex]
[tex]\[ y = -4 \][/tex]
So, the solution to the system of equations is [tex]\((0, -4)\)[/tex].
