To solve for $x$ and $y$ in the given system of equations, let's start by setting up the equations:

1. $2x - y = 17$
2. $4y + 3x = 9$

Let's go through the steps to solve these equations.

Step 1: Solve one of the equations for $y$ or $x$

Let's start by isolating $y$ in the first equation.

$2x - y = 17$ $y = 2x - 17$

Step 2: Substitute $y$ in the second equation

Now that we have $y = 2x - 17$, substitute this into the second equation:

$4(2x - 17) + 3x = 9$

Expanding and simplifying:

$8x - 68 + 3x = 9$ $11x - 68 = 9$ $11x = 77$ $x = 7$

Step 3: Substitute $x = 7$ back into the equation for $y$

Now, substitute $x = 7$ into $y = 2x - 17$:

$y = 2(7) - 17$ $y = 14 - 17$ $y = -3$

Solution

The solution to the system is: $x = 7, \quad y = -3$

Would you like further clarification or details on any step?

Here are some related questions to explore:

1. How can substitution be used to solve other systems of linear equations?
2. What alternative methods can be used to solve this system of equations?
3. How can you verify the solution of a system of equations?
4. What is the importance of consistency in systems of linear equations?
5. How would graphing these equations show the solution visually?

Tip: Always verify your solution by plugging the values back into the original equations. This helps confirm accuracy.