Daily Practice Problems

Class 10 Maths

Pair of Linear Equations in Two Variables

Class 10 Maths

Pair of Linear Equations in Two Variables

**Question 1:**

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

**Question 2:**

Find whether the given pair of linear equations is consistent or inconsistent.

3x + 2y = 8, 6x – 4y = 9

**Question 3:**

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.

**Question 4:**

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.

**Question 5:**

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.

**Question 6:**

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.

**Question 7: **

Find the value of k for which the system kx + 2y = 5 and 3x + y = 1 has

(i) a unique solution (ii) no solution

**Question 8:**

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

**Question 9: **

Solve the following pair of linear equations:

8x + 5y = 9

3x + 2y = 4

**Question 10:**

Solve:

+ =

- =

**Question 11:**

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then find value of k.

**Question 12:**

Write the number of solutions of the following pair of linear equations:

x + 2y – 8 = 0, 2x + 4y = 16

**Question 13:**

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.

**Question 14:**

In ∆ABC, ∠A = x, ∠B = 3x, and ∠C = y if 3y – 5x = 30°, show that triangle is right angled.

**Question 15:**

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.

**Question 16:**

The solution of 4x + 3y = 14 and 3x - 4y = 23 is ______.

**Question 17:**

If a pair of linear equations is consistent, then the lines will be _____.

**Question 18:**

Check whether the pair of equations

x + 3y = 6

2x – 3y = 12

is consistent. If so, solve them graphically

**Question 19:**

The graph of x = 2 is a line parallel to ____ axis.

**Question 20:**

How many solutions does the pair of equations y = 0 and y = -5 have?

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