Solve the silultaneous equations by using Graphical method
` x+ y = 7, x - y = 5`

Answer

To solve the simultaneous equations \( x + y = 7 \) and \( x - y = 5 \) using the graphical method, we will follow these steps:

### Step 1: Rewrite the equations in slope-intercept form (if necessary)
The equations are already in a suitable form for graphing:
1. \( x + y = 7 \)
2. \( x - y = 5 \)

### Step 2: Find the intercepts for each equation
#### For the first equation \( x + y = 7 \):
- **When \( x = 0 \)**:
\[ 0 + y = 7 \implies y = 7 \quad \text{(Point: (0, 7))} \]
- **When \( y = 0 \)**:
\[ x + 0 = 7 \implies x = 7 \quad \text{(Point: (7, 0))} \]

#### For the second equation \( x - y = 5 \):
- **When \( x = 0 \)**:
\[ 0 - y = 5 \implies y = -5 \quad \text{(Point: (0, -5))} \]
- **When \( y = 0 \)**:
\[ x - 0 = 5 \implies x = 5 \quad \text{(Point: (5, 0))} \]

### Step 3: Plot the points on a graph
- For the first equation \( x + y = 7 \), plot the points (0, 7) and (7, 0).
- For the second equation \( x - y = 5 \), plot the points (0, -5) and (5, 0).

### Step 4: Draw the lines
- Draw a straight line through the points (0, 7) and (7, 0) for the first equation.
- Draw another straight line through the points (0, -5) and (5, 0) for the second equation.

### Step 5: Identify the point of intersection
- The point where the two lines intersect is the solution to the simultaneous equations.
- From the graph, we can see that the lines intersect at the point (6, 1).

### Step 6: Write the solution
- Therefore, the solution to the simultaneous equations is:
\[ x = 6, \quad y = 1 \]

### Summary of the solution:
The solution to the equations \( x + y = 7 \) and \( x - y = 5 \) is \( (6, 1) \).

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