x + y x − y

To solve for $x$ and $y$ given the equations derived from the matrix system, we interpret the given equations as:

$x + y = -4$ $x - y = -16$

We solve this system of equations using either substitution or elimination. Let's use the elimination method:

Step 1: Add the two equations together

$(x + y) + (x - y) = -4 + (-16)$ $2x = -20$ $x = -10$

Step 2: Substitute $x = -10$ into one of the original equations

Using $x + y = -4$: $-10 + y = -4$ $y = -4 + 10$ $y = 6$

Final Answer:

$x = -10, \, y = 6$

Would you like to see a detailed verification or explore another method?

Here are 5 related questions to practice:

1. Solve the system $3x + 2y = 5$ and $4x - y = 7$.
2. If $x - y = 10$ and $x + 2y = 15$, find $x$ and $y$.
3. Solve $2x + 3y = 12$ and $x - y = 4$.
4. What happens if the system of equations has no solution? Provide an example.
5. Solve for $x$ and $y$ when the system is $x/2 + y = 3$ and $x - 2y = 4$.

Tip: Always simplify the system by combining like terms to reduce errors!