##### Determine graphically, the vertices of the triangle formed by the linesy = x, 3y = x and x + y = 8

Given linear equations are

y = x …(i)

3y = x …(ii)

and x + y = 8 …(iii)

For equation y = x,

If x = 1, then y = 1

If x = 0, then y = 0

If x = 2, then y = 2

Table for line y = x,

 x 0 1 2 y 6 1 2 Points O A B

For equation x = 3y,

If x = 0, then y = 0. if x = 3, then y = 1, and if x = 6, then y = 2

Table for line x = 3y,

 x 0 3 6 Y 0 1 2 Points O C D

For equation x + y = 8 or x = 8 - y

If x = 0, then y = 8, if x = 8, then y = 0 and if x = 4, then y = 4.

Table for line x + y = 8

 x 0 4 8 Y 8 4 0 Points P Q R

Plotting the points A (1, 1) and B(2,2) we get the straight line AB.

Plotting the points C (3, 1) and D(6, 2), we get the straight line CD.

Plotting the point P (0, 8), Q(4, 4) and R(8, 0), we get the straight line PQR.

We see that lines AB and CD intersecting the line PR on Q and D, respectively.

So, is formed by these lines. Hence, the vertices of the formed by the given lines are O(0, 0), Q(4, 4) and D(6,2).

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