By drawing a graph for each of the equations $3 x + y + 5 = 0$ ; $3 y - x = 5$ and $2 x + 5 y = 1$ on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point). Take $1 c m = 1$ unit on both the axes.

Point of intersection is

(0, 1)

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Point of intersection is

(2, 1)

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Point of intersection is

(- 2, 1)

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Point of intersection is

(0, - 1)

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Solution

The correct option is C Point of intersection is $(- 2, 1)$
Taking 1 cm = 1 uni
Plotting equation $3 x + y + 5 = 0$
Let $y = 4$ then,
$=> 3 x + 4 = - 5$
$=> 3 x = - 9$
$=> x = - 3$
One point is $(- 3, 4)$
Let $y = 1$ then,
$=> 3 (1) + y + 5 = 0$
$=> y = - 8$
Other point is $(1, - 8)$
Plotting equation $3 y - x = 5$
Let $y = 2$
$=> 3 (2) - x = 5$
$=> x = 1$
One point is $(1.2)$
Let $x = - 5$ then,
$=> 3 y - (- 5) = 5$
$=> y = 0$
Other point is $(- 5, 0)$
Plotting equation $2 x + 5 y = 1$
Let $x = - 2$ then,
$=> 2 (- 2) + 5 y = 1$
$=> 5 y = 1 + 5$
$=> y = 1$
One point is $(- 2, 1)$
Let $y = - 1$ then,
$=> 2 x + 5 (- 1) = 1$
$=> x = 3$
The other point is $(3, - 1)$
The point of intersection $(- 2, 1)$ and the lines given by the equations are concurrent.

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Similar questions

Q. Equation of the line passing through the point of intersection of the lines

2 x + 3 y - 5 = 0, 3 x + 2 y - 5 = 0

and having slope

- 1

Q. Find the equations to the straight lines that pass through the intersection of the lines

2 x - 3 y = 0

and

4 x - 5 y = 2

and

(i)

Passes through the point

(2, 1)

(i i)

Is perpendicular to the line

x + 2 y + 1 = 0

(i i i)

Is parallel to the line

3 x - 4 y + 5 = 0

Find the equation of the stright line passing through the point of intersection of $2 x + 3 y + 1 = 0$ and $3 x - 5 y - 5 = 0$ and equally inclined to the axes.

Q. Draw the graph of

2 x - y - 1 = 0

and

2 x + y = 9

on the same graph. Use

2 c m = 1

unit on both axes.
Write down the co-ordinates of the point of intersection of the two lines.

Q. Find the equation of the straight line passing through the point of intersection of 2x + 3y + 1 = 0 and 3x − 5y − 5 = 0 and equally inclined to the axes.

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By drawing a graph for each of the equations 3x+y+5=0; 3y−x=5 and 2x+5y=1 on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point). Take 1 cm=1 unit on both the axes.

By drawing a graph for each of the equations $3 x + y + 5 = 0$ ; $3 y - x = 5$ and $2 x + 5 y = 1$ on the same graph paper; show that the lines given by these equations are concurrent (i.e. they pass through the same point). Take $1 c m = 1$ unit on both the axes.