We have the system of equations:

$4x - 2y = 8$

$15x + 5y = 5$

Step 1: Solve for one variable

Let's solve for $y$ using the elimination method. First, multiply the first equation by 5 and the second equation by 2 to make the coefficients of $y$ equal:

$(4x - 2y) \times 5 = 8 \times 5$

$(15x + 5y) \times 2 = 5 \times 2$

This simplifies to:

$20x - 10y = 40$

$30x + 10y = 10$

Step 2: Add the Equations

$(20x - 10y) + (30x + 10y) = 40 + 10$

$50x = 50$

$x = 1$

Step 3: Substitute $x = 1$ into the First Equation

$4(1) - 2y = 8$

$4 - 2y = 8$

$-2y = 4$

$y = -2$

Final Answer:

$x = 1, \quad y = -2$

Would you like more details or a different method?

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Related Questions:

1. How do you solve a system of equations using substitution?
2. What is the determinant method for solving a system of equations?
3. How can you graphically interpret the solution of this system?
4. How do you check if the system is consistent or inconsistent?
5. What happens if the system has no solution or infinite solutions?

Tip:

Always check your solution by substituting the values back into the original equations!