The question in the image states:

"Diketahui persamaan 6x - y = 13 dan x + 3y = 7. Berapakah nilai x dan y?"

This is a system of linear equations:

1. $6x - y = 13$
2. $x + 3y = 7$

Steps to Solve:

Step 1: Express $y$ from the second equation

From $x + 3y = 7$: $3y = 7 - x$ $y = \frac{7 - x}{3}$

Step 2: Substitute $y$ into the first equation

Substitute $y = \frac{7 - x}{3}$ into $6x - y = 13$: $6x - \frac{7 - x}{3} = 13$ Eliminate the fraction by multiplying through by 3: $18x - (7 - x) = 39$ Simplify: $18x - 7 + x = 39$ $19x - 7 = 39$ $19x = 46$ $x = \frac{46}{19} \quad \text{or approximately } 2.42$

Step 3: Find $y$ using $x$

Substitute $x = \frac{46}{19}$ into $y = \frac{7 - x}{3}$: $y = \frac{7 - \frac{46}{19}}{3}$ First, find $7 - \frac{46}{19}$: $7 = \frac{133}{19}, \quad \text{so } 7 - \frac{46}{19} = \frac{133 - 46}{19} = \frac{87}{19}$ Thus: $y = \frac{\frac{87}{19}}{3} = \frac{87}{57} = \frac{29}{19}$

Final Answer:

$x = \frac{46}{19}, \quad y = \frac{29}{19}$

Or approximately: $x \approx 2.42, \quad y \approx 1.53$

Would you like me to explain any steps in detail or verify the results? 😊

Here are 5 related questions to expand understanding:

1. What is the method of substitution for solving a system of equations?
2. How does elimination work when solving linear equations?
3. What happens if a system of equations has no solution or infinite solutions?
4. Can you solve this problem graphically? How would the solution appear on a graph?
5. What is the importance of fractions when solving equations accurately?

Tip: Always simplify fractions whenever possible to make calculations easier.