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What is the solution to the system of equations?

[tex]\[
\left\{
\begin{array}{l}
2x + y = -4 \\
x - y = 4
\end{array}
\right.
\][/tex]



Answer :

GinnyAnswer
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].

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