To solve this system of equations, we have:

1. $2x - 3y = 14$
2. $2x - y = 10$

We can use the elimination or substitution method. Here, I’ll use elimination:

Step 1: Eliminate $x$ by subtracting the equations

Since both equations have the term $2x$, we can subtract the second equation from the first:

$(2x - 3y) - (2x - y) = 14 - 10$

This simplifies to:

$-2y = 4$

Step 2: Solve for $y$

Now, divide both sides by $-2$:

$y = -2$

Step 3: Substitute $y = -2$ back into one of the original equations

Let’s substitute $y = -2$ into the second equation:

$2x - (-2) = 10$

$2x + 2 = 10$

Subtract 2 from both sides:

$2x = 8$

Now, divide by 2:

$x = 4$

Solution

The solution to the system is: $x = 4, \quad y = -2$

Would you like a more detailed explanation of any step?

Here are 5 related questions to explore further:

1. How would the solution change if the constants were different in the equations?
2. What other methods could be used to solve this system of equations?
3. How can you verify that the solution is correct?
4. What happens if you add the two equations instead of subtracting them?
5. Could this system of equations be represented graphically, and what would that look like?

Tip: When solving systems of equations, elimination is often easiest when the coefficients of one variable are identical or easy to manipulate.