Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.
Find whether the given pair of linear equations is consistent or inconsistent.
3x + 2y = 8, 6x – 4y = 9
A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of boat in still water and the speed of stream.
The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.
A train covered a certain distance at a uniform speed. If the train would have been 10 faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 ; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
The age of the father is twice the sum of the ages of his 2 children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.
Find the value of k for which the system kx + 2y = 5 and 3x + y = 1 has
(i) a unique solution (ii) no solution
7x – 5y – 4 = 0 is given. Write another linear equation, so that the lines represented by the pair are:
(i) intersecting (ii) coincident (iii) parallel
Solve the following pair of linear equations:
8x + 5y = 9
3x + 2y = 4
If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then find value of k.
Write the number of solutions of the following pair of linear equations:
x + 2y – 8 = 0, 2x + 4y = 16
If x = a, y = b is the solution of the pair of equation x – y = 2 and x + y = 4, then find the value of a and b.
In ∆ABC, ∠A = x, ∠B = 3x, and ∠C = y if 3y – 5x = 30°, show that triangle is right angled.
Half the perimeter of a rectangle garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
The solution of 4x + 3y = 14 and 3x - 4y = 23 is ______.
If a pair of linear equations is consistent, then the lines will be _____.
Check whether the pair of equations
x + 3y = 6
2x – 3y = 12
is consistent. If so, solve them graphically
The graph of x = 2 is a line parallel to ____ axis.
How many solutions does the pair of equations y = 0 and y = -5 have?