A part of monthly Hostel charge is fixed and the remaining depends on the number of days one has taken food in the mess. When Swati takes food for 20 days, she has to pay 13000 as hostel charges whereas, Mansi who takes food for 25 days pays? 3500 as hostel charges. Find the fixed charges and the cost of food per day.
Find whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident: 2x – 3y + 6 = 0, 4x – 5y + 2 = 0
Given a linear equation 3x-5y = 11. Form another linear equation in these variables such that the geometric representation of the pair so formed is:
(i) intersecting lines
(ii) coincident lines
(iii) parallel lines
4 chairs and 3 tables cost? 2100 and 5 chairs and 2 tables cost? 1750. Find the cost of one chair and one table separately
Question 12.
Solve the following pair of equations by reducing them to a pair of linear equations:
Determine graphically whether the following pair of linear equations has a unique solution, infinitely many solutions or no solution
2x – 3y = 5 ;
3x + 4y = – 1
The owner of a taxi company decides to run all the taxi on CNG fuels instead of petrol/ diesel. The taxi charges in city comprise of fixed charges together with the charge for the distance covered.
For a journey of 13 km, the charge paid is? 129 and for a journey of 22 km, the charge paid is ^ 210.
(i) What will a person have to pay for traveling a distance of 32 km?
(ii) Why did he decide to use CNG for his taxi as a fuel?
At a certain time in a zoo, the number of heads and the number of legs of tiger and peacocks was counted and it was found that there were 47 heads and 152 legs. Find the number of tigers and peacocks in the zoo:
Why it is necessary to conserve these animals?
For what values of p and q will the following pair of linear equations has infinitely many solutions?
4x + 5y = 2;
(2p + 7q)x + (p + 8q)y = 2q-p + 1
For what value of k will the pair of equations have no solution?
3x + y = 1
(2k-l)x+ (k-l)y = 2k+l
For what value of p will the following system of equations has no solution;
(2p -1) x + (p -1) y = 2p + 1;
y + 3x – 1 = 0
Solve the equations graphically:
2x + y = 2;
2y-x = 4
What is the area of the triangle formed by the two lines and the lines y = 0?
Draw the graphs of the following equations: x + y — 5; x-y = 5
(i) Find the solution of the equations from the graph.
(ii) Shade the triangular region formed by the lines and the y-axis.
Find the value of k for which the following pair of linear equations have infinitely
many solutions :
2x + 3y = 7;
(k – l)x + (k + 2)y = 3k
Question 42.
For what value of k will the following pair of linear equations have no solution?
2x + 3y = 9;
6x + (k – 2)y = (3k – 2).
For what value of p will the following pair of linear equations have infinitely many solutions?
(p – 3)x + 3y = p;
px + py = 12
Find the values of a and b for which the following pair of linear equations has infinitely many solutions: 2x + 3y = 7
(3/4)(a + b)x + (2a – b)y = 21
The sum of the numerator and the denominator of a fraction is 4 more than twice the numerator. If 3 is added to each of the numerator and denominator, their ratio becomes 2 : 3. Find the fraction.
