To solve the system of equations using the addition method, let’s follow these steps:
Given equations:
[tex]\[
\begin{array}{l}
x + y = -4 \quad \text{(Equation 1)} \\
x - y = -6 \quad \text{(Equation 2)}
\end{array}
\][/tex]
Step 1: Add the two equations to eliminate [tex]\( y \)[/tex].
[tex]\[
(x + y) + (x - y) = -4 + (-6)
\][/tex]
When you add the left-hand sides of the equations together, you get:
[tex]\[
x + y + x - y = x + x = 2x
\][/tex]
And when you add the right-hand sides, you get:
[tex]\[
-4 + (-6) = -10
\][/tex]
So, the equation simplifies to:
[tex]\[
2x = -10
\][/tex]
Step 2: Solve for [tex]\( x \)[/tex].
Divide both sides of the equation by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-10}{2} = -5
\][/tex]
Step 3: Substitute [tex]\( x = -5 \)[/tex] back into one of the original equations to solve for [tex]\( y \)[/tex].
We'll use Equation 1, [tex]\( x + y = -4 \)[/tex]:
[tex]\[
-5 + y = -4
\][/tex]
To solve for [tex]\( y \)[/tex], add 5 to both sides of the equation:
[tex]\[
y = -4 + 5 = 1
\][/tex]
So, the solution to the system of equations is:
[tex]\[
(x, y) = (-5, 1)
\][/tex]
Therefore, the correct choice is:
A. The solution set is [tex]\((-5, 1)\)[/tex].
