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Exercise 4 - Pair of Linear Equations in Two Variables, Class 10, Maths PDF Download

Pair of Linear Equations in Two Variables

Exercise 4

Question: 1. Solve the following pair of linear equations by the elimination method and the substitution method:

(i) x + y = 5 and 2x – 3y = 4

Exercise 4 - Pair of Linear Equations in Two Variables, Class 10, Maths

(ii) 3x + 4y = 10 and 2x – 2y = 2

Exercise 4 - Pair of Linear Equations in Two Variables, Class 10, Maths

(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7

Exercise 4 - Pair of Linear Equations in Two Variables, Class 10, Maths
Exercise 4 - Pair of Linear Equations in Two Variables, Class 10, Maths

Question: 2. Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes ,1/2 if we only add 1 to the denominator. What is the fraction?

Exercise 4 - Pair of Linear Equations in Two Variables, Class 10, Maths

(ii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Exercise 4 - Pair of Linear Equations in Two Variables, Class 10, Maths

(iii) Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.

Exercise 4 - Pair of Linear Equations in Two Variables, Class 10, Maths
 

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FAQs on Exercise 4 - Pair of Linear Equations in Two Variables, Class 10, Maths

1. What are linear equations in two variables?
Ans. Linear equations in two variables are equations in the form of ax + by = c, where a, b, and c are constants and x and y are variables. These equations represent a straight line on a graph and have infinite solutions.
2. How do we solve a pair of linear equations?
Ans. To solve a pair of linear equations in two variables, we can use the methods of substitution, elimination, or graphical representation. In the substitution method, we solve one equation for one variable and substitute it into the other equation. In the elimination method, we eliminate one variable by multiplying one or both equations by suitable constants. Graphical representation involves plotting the equations on a graph and finding the point of intersection.
3. What does a unique solution mean for a pair of linear equations?
Ans. A pair of linear equations has a unique solution if the lines representing the equations intersect at exactly one point. This means that the values of the variables x and y satisfy both equations simultaneously and there is only one such solution.
4. Can a pair of linear equations have no solution?
Ans. Yes, a pair of linear equations can have no solution. This occurs when the lines representing the equations are parallel and do not intersect. In this case, the equations are inconsistent, and there is no value of x and y that satisfies both equations simultaneously.
5. Can a pair of linear equations have infinitely many solutions?
Ans. Yes, a pair of linear equations can have infinitely many solutions. This happens when the lines representing the equations coincide and overlap. In this case, any point on the line is a solution to the equations, and there are infinitely many such solutions.
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