From the image, the system of linear equations is as follows:

1. $5x + y = 3$
2. $-4x + 4y = 12$

Let's solve this system of equations step by step using the substitution or elimination method. I will use the elimination method.

Step 1: Simplify if possible

The second equation can be simplified by dividing the entire equation by 4: -4x + 4y = 12 \implies -x + y = 3 \tag{Equation 2'}

The simplified system of equations is:

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

Step 2: Eliminate $y$

To eliminate $y$, subtract Equation 2' from Equation 1: $(5x + y) - (-x + y) = 3 - 3$ Simplify: $5x + y + x - y = 0$ $6x = 0 \implies x = 0$

Step 3: Solve for $y$

Substitute $x = 0$ into one of the original equations, say $5x + y = 3$: $5(0) + y = 3 \implies y = 3$

Final Solution:

$x = 0, \, y = 3$

Would you like further clarification or help with graphing this solution?

Here are five related questions to expand your understanding:

1. What is the geometric interpretation of solving a system of linear equations?
2. Can you solve the system using the substitution method for verification?
3. How would the solution change if the second equation were $-4x + 4y = 15$?
4. What is the determinant of the coefficient matrix for this system, and what does it signify?
5. How would this system be solved using matrix methods (e.g., Gaussian elimination)?

Tip: Always simplify equations first (like dividing through by common factors) to make calculations easier.