To solve the system of equations:

1. $-4x + y = -29$
2. $-x + y = -2$,

we can use the substitution or elimination method. Here, we will use the elimination method.

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Step 1: Align equations for elimination

-4x + y = -29 \tag{1} -x + y = -2 \tag{2}

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Step 2: Eliminate $y$

Subtract equation (2) from equation (1): $(-4x + y) - (-x + y) = -29 - (-2)$ Simplify: $-4x + y + x - y = -29 + 2$ $-3x = -27$ Solve for $x$: $x = 9$

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Step 3: Substitute $x = 9$ into one of the original equations

Using equation (2):
$-x + y = -2$ Substitute $x = 9$:
$-(9) + y = -2$ $-9 + y = -2$ $y = 7$

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Final Solution:

$x = 9, \; y = 7$

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Would you like a graphical explanation or details on a different method?

Related Questions:

1. How can we verify solutions to systems of equations?
2. What is the difference between substitution and elimination methods?
3. How do systems of equations work graphically?
4. Can this system of equations have infinitely many solutions?
5. What is the process for solving systems of three equations?

Tip: Always check your solution by substituting back into the original equations to ensure accuracy.