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 2 cm = 1 unit on both the axes.

Question

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 2 cm = 1 unit on both the axes.

KnowledgeBoat · Accepted Answer

First equation: 3x + y + 5 = 0 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -3, then 3 (-3) + y + 5 = 0 ⇒ y = 4 Let x = -2, then 3 (-2) + y + 5 = 0 ⇒ y = 1 Let x = 1, then 3 1 + y + 5 = 0 ⇒ y = -8 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -3 | -2 | 1 --|--- |--- |--- y | 4 | 1 | -8 Step 3: Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph. Second equation: 3y - x = 5 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -2, then 3y - (-2) = 5 ⇒ y = 1 Let x = 1, then 3y - 1 = 5 ⇒ y = 2 Let x = 7, then 3y - 7 = 5 ⇒ y = 4 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -2 | 1 | 7 --|--- |--- |--- y | 1 | 2 | 4 Step 3: Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph. Third equation: 2x + 5y = 1 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -7, then 2 (-7) + 5y = 1 ⇒ y = 3 Let x = -2, then 2 (-2) + 5y = 1 ⇒ y = 1 Let x = 3, then 2 3 + 5y = 1 ⇒ y = -1 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -7 | -2 | 3 --|--- |--- |--- y | 3 | 1 | -1 Step 3: Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph. 3 From the graph, it is clear that all three lines intersect at a common point (-2, 1), confirming that the lines are concurrent.

Mathematics

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 2 cm = 1 unit on both the axes.

Graphical Solution

Related Questions

The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.
Find, graphically :
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(ii) the co-ordinates of the vertices of the triangle.

Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x + 10, y = 5x - 15.
From the graph find :
(i) the co-ordinates of the point where the two lines intersect;
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Mathematics

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 2 cm = 1 unit on both the axes.

Graphical Solution

Related Questions

The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.Find, graphically :(i) the area of triangle;(ii) the co-ordinates of the vertices of the triangle.

Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x + 10, y = 5x - 15.From the graph find :(i) the co-ordinates of the point where the two lines intersect;(ii) the area of the triangle between the lines and the x-axis.

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 2 cm = 1 unit on both the axes.

The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.
Find, graphically :
(i) the area of triangle;
(ii) the co-ordinates of the vertices of the triangle.

Using a scale of 1 cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x + 10, y = 5x - 15.
From the graph find :
(i) the co-ordinates of the point where the two lines intersect;
(ii) the area of the triangle between the lines and the x-axis.