Linear Equation in Two Variables Questions

From the pair of linear equations in the following problem and find their solutions (if they exist) by any algebraic method :

Question : From the pair of linear equations in the following problem and find their solutions (if they exist) by any algebraic method : (i)  A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student, A takes food …

From the pair of linear equations in the following problem and find their solutions (if they exist) by any algebraic method : Read More »

Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4

Solution : The given linear equations are : 8x + 5y = 9              ………..(1) 3x + 2y = 4              ………..(2) By Substitution Method : Form equation (1),  y = \(9 – 8x\over 5\) Substitute the value of y in equation (2), we get …

Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4 Read More »

For what values of a and b, the following system of equations have infinite number of solutions ?

Question : (i)  For what values of a and b, the following system of equations have infinite number of solutions ? 2x + 3y = 7 (a – b)x + (a + b)y = 3a + b – 2 (ii)  For what value of k will the following pair of linear equations have no solution …

For what values of a and b, the following system of equations have infinite number of solutions ? Read More »

Which of the following pairs of linear equations has unique solutions, no solution, or infinitely solution ? In case there is a unique solution, find it by using cross multiplication method.

Question : Which of the following pairs of linear equations has unique solutions, no solution, or infinitely solution ? In case there is a unique solution, find it by using cross multiplication method. (i)  x – 3y – 3 = 0       and      3x – 9y – 2 = 0 (ii)  2x …

Which of the following pairs of linear equations has unique solutions, no solution, or infinitely solution ? In case there is a unique solution, find it by using cross multiplication method. Read More »

From the pair of linear equation in the following problems, and find their solutions (if they exist) by the elimination method

Question : From the pair of linear equation in the following problems, and find their solutions (if they exist) by the elimination method : (i)  If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes \(1\over 2\) if we only add 1 to the denominator. …

From the pair of linear equation in the following problems, and find their solutions (if they exist) by the elimination method Read More »

Solve the following pair of linear equations by the elimination method and the substitution method

Question : Solve the following pair of linear equations by the elimination method and the substitution method : (i)  x + y = 5  and   2x – 3y = 4 (ii)  3x + 4y = 10  and  2x – 2y = 2 (iii)  3x – 5y – 4 = 0  and  9x = 2y + …

Solve the following pair of linear equations by the elimination method and the substitution method Read More »

Form the pair of linear equations for the following problems and find their solution by substitution method.

Question :  Form the pair of linear equations for the following problems and find their solution by substitution method. (i)  The difference between two numbers is 26 and one number is three times the other. Find them. (ii)  The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them. (iii)  The coach …

Form the pair of linear equations for the following problems and find their solution by substitution method. Read More »

Solve 2x + 3y = 11 and 2x – 4y = -24 and hence find the value of ‘m’ for which y = mx + 3.

Solution : We have, 2x + 3y = 11        ….(1) and 2x – 4y = -24        ……(2) From equation (1), we have 2x = 11 – 3y Substituting the value of 2x = 11 – 3y in (2), we get 11 – 3y – 4y = -24 -7y = …

Solve 2x + 3y = 11 and 2x – 4y = -24 and hence find the value of ‘m’ for which y = mx + 3. Read More »

Draw the graph of the equation x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Solution : Given Pair of linear equations are : x – y + 1 = 0 ……(i) and 3x + 2y – 12 = 0 …….(ii) first we find points for equation (i), x 0 4 y = x + 1 1 5 Points A B second we find points for equation (ii), x 0 …

Draw the graph of the equation x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region. Read More »