The system of equations provided in the image is:

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

We will solve this system of linear equations using substitution.

Step 1: Substituting $y = x + 2$ into the second equation:

$5x - 4(x + 2) = -3$

Step 2: Simplify the equation:

$5x - 4x - 8 = -3$

$x - 8 = -3$

$x = 5$

Step 3: Substitute $x = 5$ back into $y = x + 2$:

$y = 5 + 2$

$y = 7$

Final Solution:

$x = 5, \, y = 7$

Would you like further clarification on these steps or additional details?

Related Questions:

1. How can you verify the solution of a system of equations?
2. What is the graphical interpretation of solving this system of equations?
3. How do you solve this system using elimination instead of substitution?
4. What types of systems of equations have no solution or infinitely many solutions?
5. How can we extend these techniques to solve systems of three variables?

Tip:

Always substitute your solution back into the original equations to confirm it satisfies both equations.