Use the graphical method to show that the straight lines given by the equations x + y = 2, x - 2y = 5 and x/3 + y = 0 pass through the same point.

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KnowledgeBoat · Accepted Answer

First equation : x + y = 2 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -1, then (-1) + y = 2 ⇒ y = 3 Let x = 0, then 0 + y = 2 ⇒ y = 2 Let x = 1, then 1 + y = 2 ⇒ y = 1 Let x = 3, then 3 + y = 2 ⇒ y = -1 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -1 | 0 | 1 | 3 --|--- |---|---|--- y | 3 | 2 | 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. Second equation : x - 2y = 5 Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -1, then (-1) - 2y = 5 ⇒ y = -3 Let x = 0, then 0 - 2y = 5 ⇒ y = -2.5 Let x = 1, then 1 - 2y = 5 ⇒ y = -2 Let x = 3, then 3 - 2y = 5 ⇒ y = -1 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -1 | 0 | 1 | 3 --|--- |--- |---| -- y | -3 |-2.5| -2| -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. Third equation : Step 1: Give at least three suitable values to the variable x and find the corresponding values of y. Let x = -3, then ⇒ y = 1 Let x = 0, then ⇒ y = 0 Let x = 3, then ⇒ y = -1 Step 2: Make a table (as given below) for the different pairs of the values of x and y: x | -3 | 0 | 3 --|--- |---|--- y | 1 | 0 | -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. Hence, the three straight lines pass through the same point.

Mathematics

Use the graphical method to show that the straight lines given by the equations x + y = 2, x - 2y = 5 and x/3 + y = 0 pass through the same point.

Coordinate Geometry

Related Questions

Draw the graph of equation 3x - 4y = 12. Use the graph drawn to find :
(i) y₁, the value of y, when x = 4
(ii) y₂, the value of y, when x = 0.

Draw the graph of line x + y = 5. Use the graph paper drawn to find the inclination and the y-intercept of the line.

Draw the graph of line 2x + y = 5.

Mathematics

Use the graphical method to show that the straight lines given by the equations x + y = 2, x - 2y = 5 and x/3 + y = 0 pass through the same point.

Coordinate Geometry

Related Questions

Draw the graph of equation 3x - 4y = 12. Use the graph drawn to find :(i) y1, the value of y, when x = 4(ii) y2, the value of y, when x = 0.

Draw the graph of line x + y = 5. Use the graph paper drawn to find the inclination and the y-intercept of the line.

Draw the graph of line 2x + y = 5.

Draw the graph of equation 3x - 4y = 12. Use the graph drawn to find :
(i) y₁, the value of y, when x = 4
(ii) y₂, the value of y, when x = 0.