To find the values of $x$ and $y$, we can solve the system of equations:

1. $3x - 2y = -21$
2. $x = 3y - 14$

Step 1: Substitute the expression for $x$ from equation (2) into equation (1).

From equation (2), $x = 3y - 14$. Substituting this into equation (1):

$3(3y - 14) - 2y = -21$

Step 2: Expand and simplify the equation.

$9y - 42 - 2y = -21$

Combine like terms:

$7y - 42 = -21$

Step 3: Solve for $y$.

Add 42 to both sides:

$7y = 21$

Now, divide both sides by 7:

$y = 3$

Step 4: Solve for $x$.

Substitute $y = 3$ into equation (2):

$x = 3(3) - 14$ $x = 9 - 14$ $x = -5$

Final Answer:

• $x = -5$
• $y = 3$

Do you want more details or have any questions?

Related Questions:

1. How can you solve systems of equations using substitution?
2. What is the elimination method for solving systems of equations?
3. Can a system of equations have no solution or infinite solutions?
4. How can you graphically solve a system of equations?
5. What are linear equations and how are they different from non-linear equations?

Tip: When solving systems of equations, it's good to check your answers by substituting them back into the original equations.