Question

Find graphically the vertices of the triangle, whose sides have the equations 2y - x = 8, 5y -x = 14 and y = 2x - 1.

Answer 1

The given equation are :
2y - x = 8    ...(1)
5y - x = 14  ...(2)
y = 2x + 1   ...(3)
2y - x = 8
⇒ x = 2y - 8
Corresponding values of x and y can be tabulated as :

x	-4	-2	0
y	2	3	4

Plotting points (-4, 2), (-2, 3), (0, 4) and joining them, we get a line l₁ which is the graph of equation (1).
Again, 5y - x = 14
⇒ x = 5y - 14
Corresponding values of x and y can be tabulated as :

x	-4	-2	0
y	2	3	4

Plotting points (-4, 2), (1, 3), (6, 4) and joining them, we get a line l₂ which is the graph of equation (2).
Again, y = 2x + 1
Corresponding values of x and y can be tabulated as :

x	0	1	2
y	1	3	5

Plotting points (0, 1), (1, 3), (2, 5) and joining them, we get a line l₃ which is the graph of equation (3).

It can be seen that the lines l₁, l₂, and l₃ intersect each other form a triangle.
The vertices of ΔABC are A(-4, 2), B(1, 3) and C(2, 5).