Determine graphically the vertices of a triangle, the equations of whose sides are given as follows: 2y-x=8, 5y-x=14 and -2x+y=1.

# Determine graphically the vertices of a triangle, the equations of whose sides are given as follows: 2y-x=8, 5y-x=14 and -2x+y=1.

1. A
(-4, 2), (1, 3) and (2, 5)
2. B
(-2, 4), (1, 3) and (2, 5)
3. C
(-4, 2), (-1, 3) and (2, 5)
4. D
None of these

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### Solution:

Give pair of linear equations   and  .......... (3)
To find the vertices of a triangle graphically, we will solve the equations in any one variable and make the table for the values of coordinates.
Solving the equation (1), writing y in terms of x and making the table for the co-ordinates.
2y=8+x
${⇒}{y}{=}\frac{{8}{+}{x}}{{2}}$
 x y -4 2 2 5
Solving the equation (2), write in y terms and make the table for the co-ordinates.
${⇒}{5}{y}{-}{x}{=}{14}$
${⇒}{y}{=}\frac{{14}{+}{x}}{{5}}$
 x y 1 3 -4 2
Solving the equation (3), write in y terms and make the table for the co-ordinates.
${⇒}{-}{2}{x}{+}{y}{=}{1}$
${⇒}{y}{=}{1}{+}{2}{x}$
 x y 1 0 2 5
Plotting all the points on the graph.
From the graph, it is observed that the lines taken in pairs intersect each other at points A(-4,2), B(1,3) and C(2,5).
Hence, the vertices of the triangle ABC are A(-4,2), B(1,3) and C(2,5).
Hence, option (1) is correct.

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