Let's solve the system of equations using elimination.

The equations provided are:

1. $-5x - 4y = 4$
2. $x + y = 1$

Step 1: Align the equations

We can rewrite the second equation to make substitution or elimination simpler: $x + y = 1 \implies x = 1 - y$

Step 2: Substitute or eliminate

We substitute $x = 1 - y$ into the first equation: $-5(1 - y) - 4y = 4$

Simplify: $-5 + 5y - 4y = 4$ $-5 + y = 4$ $y = 9$

Step 3: Solve for $x$

Using $x + y = 1$: $x + 9 = 1$ $x = -8$

Final Answer:

The solution is: $(x, y) = (-8, 9)$

Would you like more clarification or assistance?

Here are 5 related questions for practice:

1. What is substitution in solving systems of equations, and how does it differ from elimination?
2. Solve the system using substitution: $2x + 3y = 6$ and $x - y = 4$.
3. How do you decide whether to use substitution or elimination for a given system of equations?
4. Solve $-3x + 5y = 7$ and $x + y = 2$ using elimination.
5. How can graphing verify the solution to a system of linear equations?

Tip: Always check your solution by substituting both values back into the original equations!