NCERT Solutions of Pair of Linear Equations in Two Variables Class 10
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Pair of Linear Equations in Two Variables

NCERT Solution

Exercise 3.2 - Part -II(NCERT)

Question 4 - Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically.

class ten math cbse - Pair of Linear equations in two variables_32, exercise 3.2 - ncert solution

Solution: For the given pair of linear equations;

class ten math cbse - Pair of Linear equations in two variables_33, exercise 3.2 - ncert solution

It is clear that;

class ten math cbse - Pair of Linear equations in two variables_34, exercise 3.2 - ncert solution

Hence the given pair of linear equations is dependent and consistent. The lines for the equations will be coincident. This means there would be infinitely many solutions for the given pair of linear equations.

class ten math cbse - Pair of Linear equations in two variables_35, exercise 3.2 - ncert solution

Solution: For the given pair of linear equations;

class ten math cbse - Pair of Linear equations in two variables_36, exercise 3.2 - ncert solution

It is clear that;

class ten math cbse - Pair of Linear equations in two variables_37, exercise 3.2 - ncert solution

Hence the given pair of linear equations is inconsistent.

class ten math cbse - Pair of Linear equations in two variables_38, exercise 3.2 - ncert solution

Solution: For the given pair of linear equations;

class ten math cbse - Pair of Linear equations in two variables_39, exercise 3.2 - ncert solution

It is clear that;

class ten math cbse - Pair of Linear equations in two variables_40, exercise 3.2 - ncert solution

Hence the given pair of linear equations is consistent.

Following graph can be plotted with the given pair of linear equations;

class ten math cbse - Pair of Linear equations in two variables_41, exercise 3.2 - ncert solution

Value of x = 2 and that of y = 2

class ten math cbse - Pair of Linear equations in two variables_42, exercise 3.2 - ncert solution

Solution: For the given pair of linear equations;

class ten math cbse - Pair of Linear equations in two variables_43, exercise 3.2 - ncert solution

It is clear that;

class ten math cbse - Pair of Linear equations in two variables_44, exercise 3.2 - ncert solution

Hence the given pair of linear equations is inconsistent.

Question 5 - Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Solution: Let us assume that width of garden = x and length = y. Then as per question;

class ten math cbse - Pair of Linear equations in two variables_45, exercise 3.2 - ncert solution

Substitution the value of y from equation (1) in equation (2) we get;

class ten math cbse - Pair of Linear equations in two variables_46, exercise 3.2 - ncert solution

Hence, length = 20 m and breadth = 16 m

Question 6 - Given the linear equation class ten math cbse - Pair of Linear equations in two variables_47, exercise 3.2 - ncert solution write another linear equation in two variables such that the geometrical representation of the pair so formed is:

(a) Intersecting lines

Solution: For intersecting line, the linear equations should meet following condition:

class ten math cbse - Pair of Linear equations in two variables_48, exercise 3.2 - ncert solution

For getting another equation to meet this criterion, multiply the coefficient of x with any number and multiply the coefficient of y with any other number. A possible equation can be as follows:

class ten math cbse - Pair of Linear equations in two variables_49, exercise 3.2 - ncert solution

(b) Parallel lines

Solution: For parallel lines, the linear equations should meet following condition:

class ten math cbse - Pair of Linear equations in two variables_50, exercise 3.2 - ncert solution

For getting another equation to meet this criterion, multiply the coefficients of x and y with the same number and multiply the constant term with any other number. A possible equation can be as follows:

class ten math cbse - Pair of Linear equations in two variables_51, exercise 3.2 - ncert solution

(c) Coincident lines

Solution: For getting coincident lines, the equations should meet following condition;

class ten math cbse - Pair of Linear equations in two variables_52, exercise 3.2 - ncert solution

For getting another equation to meet this criterion, multiply the whole equation with any number. A possible equation can be as follows:

class ten math cbse - Pair of Linear equations in two variables_53, exercise 3.2 - ncert solution

Question 7 - Draw the graphs of the equations class ten math cbse - Pair of Linear equations in two variables_54, exercise 3.2 - ncert solution Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Solution: Following graph can be plotted with the given pair of linear equations:

class ten math cbse - Pair of Linear equations in two variables_55, exercise 3.2 - ncert solution

The coordinates of vertices of the triangle are; (-1, 0), (2, 3) and (4, 0)


     
NCERT Solutions of Pair of Linear Equations in Two Variables Class 10
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