To solve this system by substitution, we can substitute $y = -x$ from the first equation into the second equation.

Given:

1. $y = -x$
2. $y = -4x + 12$

Step 1: Substitute $y = -x$ into the second equation

$-x = -4x + 12$

Step 2: Solve for $x$

Add $4x$ to both sides: $3x = 12$ Now, divide by 3: $x = 4$

Step 3: Substitute $x = 4$ back into the first equation to find $y$

$y = -4$

Solution

The solution to the system is: $(x, y) = (4, -4)$

Would you like further details, or do you have any questions?

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Here are some related questions you might explore:

1. How does substitution work for systems with both linear and quadratic equations?
2. What happens if both equations represent the same line?
3. Can substitution be used with inequalities in a system?
4. How does substitution differ from the elimination method?
5. What are some real-world applications of systems of linear equations?

Tip: When solving systems by substitution, always check the solution by plugging both values back into the original equations to confirm.