Use graph paper for this question. Take 2 cm =2 units onx-axis and 2cm=1 unit on y-axis.
solve graphically the following equations:
`3x+5y=12, 3x-5y+18=0`
(Plot only three points per line)

Answer

To solve the given equations graphically, we will follow these steps:

### Step 1: Rewrite the equations in slope-intercept form
We have the equations:
1. \(3x + 5y = 12\)
2. \(3x - 5y + 18 = 0\) which can be rewritten as \(3x - 5y = -18\)

### Step 2: Find points for the first equation \(3x + 5y = 12\)
To find points for this equation, we can choose different values for \(x\) and solve for \(y\).

- **Point 1**: Let \(x = 0\)
\[ 3(0) + 5y = 12 \implies 5y = 12 \implies y = \frac{12}{5} = 2.4 \]
So, the point is \((0, 2.4)\).

- **Point 2**: Let \(x = 4\)
\[ 3(4) + 5y = 12 \implies 12 + 5y = 12 \implies 5y = 0 \implies y = 0 \]
So, the point is \((4, 0)\).

- **Point 3**: Let \(x = -1\)
\[ 3(-1) + 5y = 12 \implies -3 + 5y = 12 \implies 5y = 15 \implies y = 3 \]
So, the point is \((-1, 3)\).

### Step 3: Find points for the second equation \(3x - 5y = -18\)
Similarly, we can choose different values for \(x\) and solve for \(y\).

- **Point 1**: Let \(x = 0\)
\[ 3(0) - 5y = -18 \implies -5y = -18 \implies y = \frac{18}{5} = 3.6 \]
So, the point is \((0, 3.6)\).

- **Point 2**: Let \(x = 4\)
\[ 3(4) - 5y = -18 \implies 12 - 5y = -18 \implies -5y = -30 \implies y = 6 \]
So, the point is \((4, 6)\).

- **Point 3**: Let \(x = -6\)
\[ 3(-6) - 5y = -18 \implies -18 - 5y = -18 \implies -5y = 0 \implies y = 0 \]
So, the point is \((-6, 0)\).

### Step 4: Plot the points on graph paper
Using the scale provided (2 cm = 2 units on the x-axis and 2 cm = 1 unit on the y-axis), plot the points for both equations:

- For the first equation \(3x + 5y = 12\):
- \((0, 2.4)\)
- \((4, 0)\)
- \((-1, 3)\)

- For the second equation \(3x - 5y = -18\):
- \((0, 3.6)\)
- \((4, 6)\)
- \((-6, 0)\)

### Step 5: Draw the lines
Connect the points for each equation with a straight line.

### Step 6: Identify the intersection point
The point where the two lines intersect is the solution to the system of equations.