These notes for CBSE Class 10 Mathematics, Chapter 3, cover Pair of Linear Equations in Two Variables. A linear equation in two variables x and y is defined as ax + by + c = 0, where a, b, and c are real numbers and neither a nor b is zero. The general form for a pair of linear equations is presented. The notes explain the graphical representation of these equations, including conditions for a unique solution (consistent pair), no solution (inconsistent pair), and infinite solutions (dependent consistent pair). Algebraic methods for solving these equations are also detailed: substitution method, elimination method, and cross-multiplication method. The notes include solved examples and practice problems for levels 1, 2, and 3, covering concepts like finding values of constants for specific solution types and solving word problems. These notes are ideal for quick revision before exams.
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? An equation of the form ax + by + c = 0, where a, b, c are real nos (a ? 0, b ? 0) is called a inear
equation in two variables x and y.
? The general form for a pair of linear equations in two variables x and y is
? Graphical representation of a pair of linear equations in two variables:
i.e. unique solution. And this type of equations are called consistent pair of linear equations.
Ex: x – 2y = 0
3x + 4y – 20 = 0
(iv) Algebraic methods of solving a pair of linear equations:
(i) Substitution method
(ii) Elimination Method
(iii) Cross multiplication method
8. For what value of k the following pair has infinite number of solutions.
(k-3)x + 3y = k
k(x+y)=12
Ans: k= 6
1. 5 pencils and 7pens together cost Rs. 50 whereas 7 pencils and 5 pens together cost Rs. 46. Find the
cost of one pencil and that of one pen.
Ans: Cost of one pencil = Rs. 3
Cost of one pen = Rs. 5
2. Solve the equations:
3x – y = 3
7x + 2y = 20
Ans: x=2, y=3
3. Find the fraction which becomes to 2/3 when the numerator is increased by 2 and equal to 4/7
when the denominator is increased by 4
Ans: 28/45
4. Solve the equation:
px + qy = p – q
qx – py = p + q
Ans: x = 1, y = -1
1. Solve the equation using the method of substitution:
3. Solve the equations by using the method of cross multiplication:
4. A man has only 20 paisa coins and 25 paisa coins in his purse, If he has 50 coins in all totaling Rs. 11.25, how many coins of each kind does he have.
Ans. 25 coins of each kind
5. For what value of k, will the system of equations
A linear equation in two variables x and y is an equation of the form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not equal to zero.
The algebraic methods to solve a pair of linear equations are the substitution method, elimination method, and cross-multiplication method.
A pair of linear equations is called consistent if it has at least one solution. This includes cases with a unique solution or infinite solutions.
Graphically, if the lines intersect at one point, there's a unique solution. If the lines are parallel, there's no solution. If the lines coincide, there are infinite solutions.
For equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, infinite solutions exist if a1/a2 = b1/b2 = c1/c2.
Yes, these notes cover the key concepts and methods for Pair of Linear Equations in Two Variables, making them suitable for revision.
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