You have the following system of linear equations:

1. $-x + y = -2$
2. $4x + y = -7$

Let's solve this system using the substitution or elimination method. I’ll use the substitution method here.

Step 1: Solve one equation for one variable

From the first equation $-x + y = -2$, we can solve for $y$:

$y = x - 2$

Step 2: Substitute into the second equation

Now, substitute $y = x - 2$ into the second equation $4x + y = -7$:

$4x + (x - 2) = -7$

Step 3: Solve for $x$

Simplify the equation:

$4x + x - 2 = -7$

$5x - 2 = -7$

Add 2 to both sides:

$5x = -5$

Now, divide both sides by 5:

$x = -1$

Step 4: Substitute $x = -1$ back into the equation for $y$

Now, substitute $x = -1$ into $y = x - 2$:

$y = -1 - 2 = -3$

Final Answer:

The solution is $x = -1$ and $y = -3$.

Verification:

Substitute $x = -1$ and $y = -3$ into both original equations to verify:

• For the first equation: $-(-1) + (-3) = 1 - 3 = -2$ (correct)
• For the second equation: $4(-1) + (-3) = -4 - 3 = -7$ (correct)

Both are satisfied, so the solution is correct.

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Would you like to see more steps or have questions on this solution?

Here are some related questions:

1. How would you solve the system using the elimination method?
2. What would happen if we multiplied one of the equations by a constant before solving?
3. How do you solve a system of equations if one of the equations is a fraction?
4. What is the graphical interpretation of the solution to this system of equations?
5. How can this method be extended to solve systems with three variables?

Tip: If you can easily express one variable in terms of the other (like we did with $y = x - 2$), substitution is often the quickest method!