- What is Linear equations
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- Linear equations Solutions
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- Graphical Representation of Linear equation in one and two variable
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- Steps to Draw the Given line on Cartesian plane
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- Simultaneous pair of Linear equation
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- Algebraic Solution of system of Linear equation
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- Simultaneous pair of Linear equation in Three Variable
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- Steps to solve the Linear equations

- NCERT Solutions Exercise 3.1
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- NCERT Solutions Exercise 3.2
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- NCERT Solutions Exercise 3.3,3.4,3.5
- NCERT Solutions Exercise 3.6
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- NCERT Solutions Exercise 3.7

- Problem and Solutions
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- Linear equations Problems
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- Linear equation worksheet
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- Linear equation word problems
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- Linear equations graphical problems

Given below are the

a. Concepts questions

b. Calculation problems

c. Multiple choice questions

d. Long answer questions

e. Fill in the blank's

In a cyclic quadrilateral ABCD,Find the four angles.

a. $\angle A = (2x + 4)$, $\angle B = (y + 3)$, $\angle C = (2y + 10)$, $\angle D = (4x -5)$.

b. $\angle A = (2x - 1)$, $\angle B = (y + 5)$, $\angle C = (2y + 15)$ and $\angle D = (4x -7)$

Solution

Given below are three equations. Two of them have infinite solutions and two have a unique solution. State the two pairs:

$3x - 2y = 4$

$6x + 2y = 4$

$9x -6y = 12$

Solution

Find the values of a and b for which the following system of linear equations has infinite number of solutions:

$2x + 3y = 7$

$2ax + (a + b)y = 28$

Solution

Find the values of a and b for which the following system of linear equations has infinite number of solutions:

$2x -3y = 7$

$(a + b)x - (a + b- 3)y = 4a + b$

Solution

In a ABC, $\angle A = x$, $\angle B = (3x -2)$, $\angle C = y$ Also $\angle C - \angle B = 9$. Find the three angles.

Solution

Find the value of k for which the system of equations x + 2y -3 = 0 and ky + 5x + 7 = 0 has a unique solution.

Solution

For what value of a the system of linear equations $2x + 3y = 7$ and $(a -1)x + (a + 1)y = 3a - 1$ represent parallel lines.

Solution

If the lines $x + 2y + 7 = 0$ and $2x + ky + 18 = 0$ intersect at a point, then find the value of k.

Solution

Is $x = 5, y = -5$ a solution of the linear equation $3x + 2y - 5 = 0$?

Solution

The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. Find the present ages of the son and the father.

Solution

Replace p by an appropriate number so that the following system of equations has a unique solution.

$2x + 3y = 5$

$px +9y = 12$

For what value of k, the following pair of linear equations has infinitely many solutions?

i. $kx + 4y - (k + 8) = 0$

$4x + ky + 4 = 0$

ii. $2x + 3y = 4$

$(k + 2)x + 6y = 3k + 2$

Solution

For what value of k, will the following system of equations have no solutions?

i. $(3k + 1) x + 3y = 2$

$(k^2 + 1) x + (k - 2) y = 5$

ii. $3x + y = 1$

$(2k - 1) x + (k - 1) y = 2k + 1$

iii. $2x + ky = 11$

$5x -7y = 5$

For what value of k, does the pair of equations given below has a unique solution?

$2x + ky = 6$

$4x + 6y = 0$

Find the value of k for which the following system of linear equations has infinite solutions:

i. $x + (k + 1) y = 5$

$(k + 1) x + 9y = 8k - 1$

ii. $8x + 5y = 9$

$kx + 10y = 18$

iii. $2x + 3y = k$

$(k - 1) x + (k + 2) y = 3k$

For what value of α, the system of equations

$ \alpha x + 3y = \alpha - 3$

$12x + \alpha y = \alpha $

will have no solution?

-6

Find the value of k for which the system

$kx + 2y = 5$

$3x + y = 1$

has (i) a unique solution, and (ii) no solution.

k ≠6 , k=6

Find the value of k for which the system

$2x + ky = 1$

$3x - 5y = 7$

has (i) a unique solution, and (ii) no solution.

k ≠ -10/3 , k=10/3

find the value of a and b for which the following system of equations has infinitely many solutions:

$2x - (2a + 5) y = 5$

$(2b + 1) x - 9y = 15$

(-1, 5/2)

Find the value of a for which the following system of equations has infinitely many solutions:

$2x + 3y - 7 = 0$

$(a - 1) x + (a + 1) y = (3a - 1)$

a=5

16) 17) 18)

Given below are the links of some of the reference books for class 10 math.

- Oswaal CBSE Question Bank Class 10 Hindi B, English Communication Science, Social Science & Maths (Set of 5 Books)
- Mathematics for Class 10 by R D Sharma
- Pearson IIT Foundation Maths Class 10
- Secondary School Mathematics for Class 10
- Xam Idea Complete Course Mathematics Class 10

You can use above books for extra knowledge and practicing different questions.

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