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


To solve the system of equations using the graphical method, we need to graph the two equations on the coordinate plane and find the point where the two lines intersect.

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

#### Equation 1: \( 4x + 6y = 2 \)

Solve for \( y \):
\[
4x + 6y = 2
\]
\[
6y = -4x + 2
\]
\[
y = -\frac{2}{3}x + \frac{1}{3}
\]
So, the first equation becomes:
\[
y = -\frac{2}{3}x + \frac{1}{3}
\]

#### Equation 2: \( 2x - y = 5 \)

Solve for \( y \):
\[
2x - y = 5
\]
\[
y = 2x - 5
\]

So, the second equation becomes:
\[
y = 2x - 5
\]

### Step 2: Graph the two equations

Now, we plot the lines:
1. \( y = -\frac{2}{3}x + \frac{1}{3} \)
   - The y-intercept is \( \left( 0, \frac{1}{3} \right) \).
   - The slope is \( -\frac{2}{3} \), meaning for every 3 units to the right, the line goes down by 2 units.
   
2. \( y = 2x - 5 \)
   - The y-intercept is \( (0, -5) \).
   - The slope is 2, meaning for every 1 unit to the right, the line goes up by 2 units.

### Step 3: Find the point of intersection

After graphing these two lines, the point where they intersect will be the solution to the system of equations. To confirm, you can solve the system algebraically.

Would you like a graph, more details, or have any other questions?

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Here are 5 relative questions to expand your understanding:

1. How can the slope help in graphing equations more efficiently?
2. What does the y-intercept represent in the context of graphing?
3. Can all systems of linear equations be solved graphically?
4. What happens if two lines are parallel when graphing a system of equations?
5. How can you verify the solution to a system of equations algebraically?

**Tip:** Always check the scales on the axes when graphing to ensure accuracy in identifying the intersection point.

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 solution covers key algebraic concepts such as slope-intercept form and finding the intersection of lines. Suitable for students in Grades 9-12.

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