Let's solve the system of equations using the elimination method.

Given system:

1. $2x - 2y = -6$
2. $5x - 2y = 3$

Step 1: Subtract the two equations

Since both equations have $-2y$, we subtract the first equation from the second:

$(5x - 2y) - (2x - 2y) = 3 - (-6)$

$5x - 2y - 2x + 2y = 3 + 6$

$(5x - 2x) + (-2y + 2y) = 9$

$3x = 9$

Step 2: Solve for $x$

$x = \frac{9}{3} = 3$

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

Using $2x - 2y = -6$:

$2(3) - 2y = -6$

$6 - 2y = -6$

$-2y = -12$

$y = \frac{-12}{-2} = 6$

Solution:

$(x, y) = (3,6)$

Would you like a detailed explanation of any step?

Related Questions:

1. How does the elimination method work in general?
2. What would happen if the coefficients of $y$ were different?
3. Can this system be solved using the substitution method?
4. How can you check if the solution is correct?
5. What does it mean if elimination results in an identity like $0 = 0$ or a contradiction like $0 = 5$?

Tip:

Always double-check your solution by plugging the values back into the original equations!