We have the system of linear equations:

1. $3x + 2y = 12$
2. $x - y = -12$

Let's solve this step by step using the substitution or elimination method.

Step 1: Solve the second equation for $x$.

From the second equation: $x - y = -12 \implies x = y - 12$

Step 2: Substitute $x = y - 12$ into the first equation.

Now, substitute $x = y - 12$ into the first equation $3x + 2y = 12$: $3(y - 12) + 2y = 12$ Distribute: $3y - 36 + 2y = 12$ Combine like terms: $5y - 36 = 12$ Add 36 to both sides: $5y = 48$ Solve for $y$: $y = \frac{48}{5}$

Step 3: Substitute $y = \frac{48}{5}$ back into $x = y - 12$.

Now that we have $y = \frac{48}{5}$, substitute this value into the expression for $x$: $x = \frac{48}{5} - 12$ Convert 12 to a fraction with denominator 5: $x = \frac{48}{5} - \frac{60}{5} = \frac{-12}{5}$

Solution:

The solution to the system of equations is: $x = \frac{-12}{5}, \quad y = \frac{48}{5}$

Would you like further details or have any questions?

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Here are 5 related questions:

1. How do you solve a system of equations using the elimination method?
2. Can you solve a system of equations graphically?
3. What is the determinant of a system of linear equations?
4. How do you solve systems with more than two equations?
5. What is the significance of consistent and inconsistent systems?

Tip: Always double-check solutions by substituting them back into the original equations to verify correctness.