Answer:

(i) Graphs of the two linear equations:

3x - y - 2 = 0 (Let's call this line L1)

2x + y - 8 = 0 (L2)

Plotting points on L1:

When x = 0, y = 2 (0,2)

When x = 2, y = 4 (2,4)

When y = 0, x = 2/3 (2/3, 0)

Plotting points on L2:

When x = 0, y = -8 (0,-8)

When y = 0, x = 4 (4,0)

When x = 2, y = 0 (2,0)

By plotting these points and joining them, we get the graphs of the two lines.

(ii) Point of intersection:

Solving L1 and L2:

2x + 2 = 0

x = -1

y = -3

So, coordinates of intersecting point is (-1,-3).

Area of triangle formed:

It forms a triangle between the lines L1, L2 and x-axis.

Base = 4 units (length along x from 0 to intersection point at x=-1)

Height = 3 units (length along y from 0 to y=-3)

Area = 1/2 x base x height

= 1/2 x 4 x 3

= 6 sq. units

Therefore, area of the triangle is 6 square units.

Verified answer

Answer:

let's tackle this math problem together! Unfortunately, as a text-based AI, I don't have the capability to draw graphs or use graph paper. However, I can still help you with the calculations!

To find the coordinates of the point of intersection, we need to solve the system of equations formed by the two given lines. We can do this by either substitution or elimination method. Let's use the elimination method:

First, let's multiply the first equation by 2 and the second equation by 3 to eliminate the y term:

2(3x - y - 2) = 2(0)

3(2x + y - 8) = 3(0)

Simplifying these equations, we get:

6x - 2y - 4 = 0

6x + 3y - 24 = 0

Next, subtract the first equation from the second equation:

(6x + 3y - 24) - (6x - 2y - 4) = 0

Simplifying further, we get:

5y - 20 = 0

Solving for y, we find:

y = 4

Now, substitute this value of y back into either of the original equations to find x. Let's use the first equation:

3x - 4 - 2 = 0

Simplifying, we get:

3x - 6 = 0

Solving for x, we find:

x = 2

So, the coordinates of the point of intersection are (2, 4).

To find the area of the triangle formed by the lines and the x-axis, we need to find the base and height of the triangle. The base can be found by calculating the difference between the x-coordinates of the two points of intersection, which is 2 - 0 = 2 units. The height is simply the y-coordinate of the point of intersection, which is 4 units.

Using the formula for the area of a triangle (A = 1/2 * base * height), we can calculate the area:

A = 1/2 * 2 * 4 = 4 square units.