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The image contains a system of linear equations and asks to solve it using two methods: elimination and substitution. The system of equations is:

1. \( 2y - 3x = 15 \)
2. \( 4y + x = 16 \)

### a) Elimination Method:
1. We will try to eliminate one variable. Let's eliminate \( x \). To do this, we'll multiply the second equation by 3 so that the coefficients of \( x \) in both equations match:

   \[
   2y - 3x = 15 \quad \text{(Equation 1)}
   \]
   \[
   3(4y + x) = 3(16) \quad \Rightarrow \quad 12y + 3x = 48 \quad \text{(New Equation 2)}
   \]

2. Now, add the two equations to eliminate \( x \):

   \[
   (2y - 3x) + (12y + 3x) = 15 + 48
   \]
   \[
   14y = 63 \quad \Rightarrow \quad y = \frac{63}{14} = 4.5
   \]

3. Substitute \( y = 4.5 \) into one of the original equations (let’s use Equation 2):

   \[
   4(4.5) + x = 16 \quad \Rightarrow \quad 18 + x = 16
   \]
   \[
   x = 16 - 18 = -2
   \]

So the solution to the system is \( x = -2 \) and \( y = 4.5 \).

### b) Substitution Method:
1. From Equation 2, solve for \( x \):

   \[
   x = 16 - 4y
   \]

2. Substitute this expression for \( x \) into Equation 1:

   \[
   2y - 3(16 - 4y) = 15
   \]
   \[
   2y - 48 + 12y = 15 \quad \Rightarrow \quad 14y = 63
   \]
   \[
   y = 4.5
   \]

3. Substitute \( y = 4.5 \) back into \( x = 16 - 4y \):

   \[
   x = 16 - 4(4.5) = 16 - 18 = -2
   \]

The solution is again \( x = -2 \) and \( y = 4.5 \).

### Graphing with Excel:
To graph this system in Excel:
1. Plot each equation by solving for \( y \) in terms of \( x \).
   - For the first equation, \( 2y = 3x + 15 \) or \( y = \frac{3x + 15}{2} \).
   - For the second equation, \( 4y = -x + 16 \) or \( y = \frac{-x + 16}{4} \).
2. Plot these lines on an XY chart in Excel, and the intersection point will give the solution \( (x, y) = (-2, 4.5) \).

Would you like me to provide further details or assistance with Excel graphing?

Here are 5 related questions to explore further:
1. What happens if the lines are parallel in a system of linear equations?
2. How can you verify the solution to a system of equations graphically?
3. Can elimination and substitution methods always be used for any system of linear equations?
4. How can you handle systems with three or more equations?
5. What is the geometric interpretation of solving linear systems in 3D space?

**Tip:** Always double-check your work by substituting the solution back into both original equations to ensure correctness.

Tentukanlah himpunan penyelesaian dari sistem persamaan linier berikut ini dengan metode a) eliminasi dan b) substitusi dan buat grafik dengan excel: persamaan 1: 2y - 3x = 15, persamaan 2: 4y + x = 16.

Learn how to solve the system of linear equations 2y - 3x = 15 and 4y + x = 16 using both elimination and substitution methods. Also, graph the equations using Excel for a clear visual representation. Suitable for students in Grades 9-12.

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