Let's solve the system of equations from the image:

$x - y = 6$ $x + 3y = -6$

Step 1: Solve for $x$ in terms of $y$ from the first equation:

From the first equation: $x - y = 6 \quad \Rightarrow \quad x = y + 6$

Step 2: Substitute this expression for $x$ into the second equation:

Substitute $x = y + 6$ into the second equation: $(y + 6) + 3y = -6$ Simplify: $y + 6 + 3y = -6$ $4y + 6 = -6$ Subtract 6 from both sides: $4y = -12$ Now solve for $y$: $y = \frac{-12}{4} = -3$

Step 3: Solve for $x$:

Now substitute $y = -3$ into $x = y + 6$: $x = -3 + 6 = 3$

Solution:

The solution to the system is $x = 3$ and $y = -3$.

Correct Answers:

• x-coordinate is 3
• y-coordinate is -3

Would you like further clarification on any of the steps, or do you have other questions?

Here are some related questions for you:

1. How do you solve a system of equations using substitution?
2. What are the different methods for solving systems of linear equations?
3. What does it mean for a system of equations to have no solution, one solution, or infinitely many solutions?
4. How can you check the solution to a system of equations?
5. How can you use the elimination method to solve this system?

Tip: When solving systems of equations, it can be helpful to check your solution by substituting the values of $x$ and $y$ back into the original equations to ensure they satisfy both equations.