Solve the system using graphical method:    
	{■( 4x+6y=2@2x-y=5)┤


To solve the system of equations graphically, follow these steps:

### Given system of equations:
1. \( 4x + 6y = 2 \)
2. \( 2x - y = 5 \)

### Step 1: Rewrite each equation in slope-intercept form (i.e., \( y = mx + b \)).

#### For the first equation:
\[ 4x + 6y = 2 \]
Solve for \( y \):
\[
6y = -4x + 2 \quad \text{(subtract \(4x\) from both sides)}
\]
\[
y = -\frac{4}{6}x + \frac{2}{6} \quad \text{(divide everything by 6)}
\]
\[
y = -\frac{2}{3}x + \frac{1}{3}
\]
So, the first equation is \( y = -\frac{2}{3}x + \frac{1}{3} \).

#### For the second equation:
\[ 2x - y = 5 \]
Solve for \( y \):
\[
-y = -2x + 5
\]
\[
y = 2x - 5 \quad \text{(multiply through by -1)}
\]
So, the second equation is \( y = 2x - 5 \).

### Step 2: Graph both equations on the same coordinate plane.

1. **For the first equation** \( y = -\frac{2}{3}x + \frac{1}{3} \):
   - The y-intercept is \( \left( 0, \frac{1}{3} \right) \).
   - The slope is \( -\frac{2}{3} \), which means for every 3 units you move to the right, you move 2 units down.

2. **For the second equation** \( y = 2x - 5 \):
   - The y-intercept is \( (0, -5) \).
   - The slope is 2, which means for every 1 unit you move to the right, you move 2 units up.

### Step 3: Find the intersection point.
Graph both lines and observe where they intersect. The coordinates of the intersection point represent the solution to the system of equations.

Let me know if you'd like me to generate a visual representation of the graph or if you need further assistance in calculating the exact intersection! 

---
Do you want me to plot the graph or give more details on graphing? Here are 5 related questions to practice:

1. How do you find the slope of a line between two points?
2. Can all systems of equations be solved graphically?
3. What happens if two lines are parallel when solving graphically?
4. How can you check a solution of a system of equations algebraically?
5. How do you find the x-intercept of a line?

**Tip:** When solving graphically, make sure the scales on both axes are consistent to ensure accuracy.

Solve the system using graphical method: {■( 4x+6y=2@2x-y=5)┤

Learn how to solve the system of linear equations 4x + 6y = 2 and 2x - y = 5 using the graphical method. This detailed step-by-step guide covers key algebraic concepts, slope-intercept form, and graphing techniques for finding the solution of the system. Ideal for students in Grades 9-11.

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