Question

Solve the following system of linear equations graphically : 3x + y – 11= 0 and x – y-1= 0
Shade the region bounded by these lines and y-axis. Also, find the area of the region bounded by the these lines and y-axis.

Answer 1

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The coordinate of the points where the line cut y axis is (3,2 )

Answer 2

Given:  System  of linear equations:   3x + y – 11 = 0………..(1) x – y - 1 = 0………..(2)

 

Solution :

For eq 1 :  

When x = 0 ,then y = 11

When x =  3 , then y = 2

3x + y – 11 = 0 passes through (0, 11) and (3, 2)

 

For eq 2 :  

When x = 0 ,then y = - 1

When x = 3 , then y = 2

x – y - 1 = 0 passes through (0, -1) , (3, 2)

Two lines intersect at a point A (3,2) .

Hence x is 3 and y is 2.

These two lines meet x axis at B (0,11) and C(0,-1)

Area of shaded region  = Area of ABC

Area of shaded region= ½ base × height  

Area of shaded region = ½ BC × AD

Area of shaded region = ½ × 12 × 3

[from graph BC = 12 and AD = 3 ]

Area of shaded region = 18 sq units .

Hence , Area of the region bounded by these two lines is 18 sq units.

Table and the Graph of the given  systems of equations are  in the  attachment below :  

Method to draw a graph :

To draw the graph of a linear equation in two variable a series of steps to be followed which is given below:

Step I:Obtain the linear equation.  Let the equation be  ax + by + c = 0

Step II: Express one unknown quantity in terms of other here. Express y in terms of x to get y = - (ax + c /b)

Step III: For any two values of x, calculate the corresponding values of y  from the expression in step II to obtain two solutions say (x1, y1 and( x2 ,y2)

Step IV: plot the points  (x1, y1 and( x2 ,y2)  on graph paper on a suitable scale.

Step V:Draw a  line passing through points marked in step IV. The line so obtained is the graph of the equation  ax + by + c = 0  

HOPE THIS ANSWER WILL HELP YOU……

 

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