Solve graphically the pair of linear equations `5x – y = 5` and `3x – 2y = – 4 `
Also find the co-ordinates of the points where these lines intersect y-axis

Answer

To solve the pair of linear equations \(5x - y = 5\) and \(3x - 2y = -4\) graphically, we will follow these steps:

### Step 1: Rewrite the equations in slope-intercept form
We start by rewriting both equations in the form \(y = mx + b\).

1. For the first equation \(5x - y = 5\):
\[ -y = -5x + 5 \implies y = 5x - 5 \]

2. For the second equation \(3x - 2y = -4\):
\[ -2y = -3x - 4 \implies 2y = 3x + 4 \implies y = \frac{3}{2}x + 2 \]

### Step 2: Find points for each line
Next, we will find points for each line by substituting values for \(x\).

**For the first equation \(y = 5x - 5\)**:
- If \(x = 0\):
\[ y = 5(0) - 5 = -5 \quad \text{(Point: (0, -5))} \]
- If \(x = 1\):
\[ y = 5(1) - 5 = 0 \quad \text{(Point: (1, 0))} \]
- If \(x = 2\):
\[ y = 5(2) - 5 = 5 \quad \text{(Point: (2, 5))} \]

**For the second equation \(y = \frac{3}{2}x + 2\)**:
- If \(x = 0\):
\[ y = \frac{3}{2}(0) + 2 = 2 \quad \text{(Point: (0, 2))} \]
- If \(x = 1\):
\[ y = \frac{3}{2}(1) + 2 = \frac{7}{2} \quad \text{(Point: (1, 3.5))} \]
- If \(x = 2\):
\[ y = \frac{3}{2}(2) + 2 = 5 \quad \text{(Point: (2, 5))} \]

### Step 3: Plot the points on a graph
Now, we will plot the points we found on a graph.

- For the first line, plot the points: (0, -5), (1, 0), and (2, 5).
- For the second line, plot the points: (0, 2), (1, 3.5), and (2, 5).

### Step 4: Draw the lines
Connect the points for each equation to form straight lines.

### Step 5: Identify the intersection point
From the graph, we can see that the two lines intersect at the point \((2, 5)\). This is the solution to the system of equations.

### Step 6: Find the coordinates where the lines intersect the y-axis
The y-axis is where \(x = 0\).

- For the first equation \(5x - y = 5\):
- The intersection with the y-axis is at the point \((0, -5)\).

- For the second equation \(3x - 2y = -4\):
- The intersection with the y-axis is at the point \((0, 2)\).

### Final Answer
The solution to the system of equations is \((2, 5)\), and the coordinates where the lines intersect the y-axis are \((0, -5)\) and \((0, 2)\).

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