Important Questions for CBSE Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables 2024-25

Class 10 is a crucial year for every student's career and an important step towards their future. No matter which subject the student wants to study, it is impossible to accomplish the year without proper concentration and knowledge. 

Every year, thousands of students choose mathematics for their career and fail to score good grades due to lack of practice. Mathematics requires daily exercise and a routine that every student should follow. 

Without proper practice, it is not possible to understand where to place which formula and solve the problems. Here, we have assembled extra questions for class 10 maths chapter 3. 

These PDF questions are prepared by Vedantu experts and are free for the students to download and practice. The teachers have prepared the question-answer set for the students according to new CBSE guidelines. The students can easily cover the entire chapter and all sorts of questions coming for their final exams. These questions cover most of the topics and are extremely reliable. It will boost your confidence and help you solve all types of questions that the examiners can set. 

Chapter 3 Maths Class 10 Important Questions

Mathematics is not an easy subject that anyone can solve just by studying before a few days of examination. Especially, class 10 is crucial with high-level mathematics problems for the students to solve. Therefore, daily practices will help students memorize the formulas and understand the types of issues that might come up during their finals. Expert mathematicians of Vedantu have prepared a set of important questions of chapter 3 Maths class 10, which will help the students revise the chapter easily. The pdf is free for the students who register for the site. 

What are Linear Equations?

Equations with first order are known as linear equations. The word linear defines the equation is in a line of the coordinate system. Therefore, any equation lying in a straight line is known as a linear equation. y=mx+b resembles the definition of a straight line where b is the intercept and m is the slope of the line. These equations consist of the highest exponent of variables as one and hence, are known as first-degree equations.

There are various types of linear equations. When an equation has only one variable or a homogeneous variable, then that type is known as a linear equation with one variable. In other words, an equation in a line is achieved by relating zero to any field of linear polynomial from which we can obtain the coefficients id known as a linear equation with one variable. 

The answers of linear equations produce values that make a true equation when exchanged with unknown values. There is only one solution available for one variable, like x+2=0. However, when it comes to two variables linear equation, the Euclidean plane's answer is calculated as Cartesian coordinates. 

Forms of Linear Equation

A line is determined in an X-Y plane through various forms. Here, we have a list of some common conditions which we use to solve linear equations. 

• Slope Intercept Form

• General Form

• Intercept Form

• Two-point Form

• Point Form

The Standard Form of Linear Equations

The combination of variables and constants form a linear equation. A linear equation with one variable is depicted as ax+b=0, where x is a variable, and a≠0. 

The standard form of linear equation with two variables is depicted as ax+by+c=0, where a is not equal to zero, b is not equal to zero, and x and y are variables. 

The standard form of a linear equation with three variables is depicted as ax+by+cz+d=0, where a, b and c are not equal to zero and x, y, z are variables. 

• Slope Intercept Form

The most common way to solve linear equations is in the slope-intercept form. It is represented as y=mx+c, where y and x are the x-y plane points, c is the intercept with a constant value and m is the slope of the line known as a gradient. 

For example, y=5x+9

Slope, m=5, and intercept=9.

• Point Slope Form

Considering the points on the x-y plane, a straight line equation is formed as the linear equation. It is represented as y-1=m(x-x1), where the coordinates of the line are x1 and y1. The other way of representing it is y=mx+y1-mx1.

• Intercept Form

The intercept form is represented when the axes of the lines intersect in two different points on the x-y plane and are neither parallel to the y-axis or the x-axis. In the equation, x/x0+y/y0=1, the values of x0 and y0 are not equal to zero. 

• Two Point Form

Suppose (x1,y1) and (x2,y2) are two points, and only one line passes through these points, then the linear equation is represented as 

y-y1=[(y2-y1)/(x2-x1)](x-x1) where x1≠x2 and (y2-y1)/(x2-x1) is the slope of the line.

Solving Linear Equations with One Variable

To solve a linear equation, you must balance both sides of the equation. When you place the equality sign in between the equation, it denotes that the value on both sides of the equation is equal. The balanced equation requires specific ways of solving it as you cannot change anyone side's value. To find the value of x, the first step is to simplify both sides and then put all the x consonants on one side, finding out the value of x. 

Solving Linear Equations with Two Variables

There are different methods that you can use to solve linear equations with two variables. 

• Substitution method

• Cross multiplication method

• Elimination method

• Determinant methods

When looking for values of the variables like x and y, it is important to solve two sets of equations. Since a single equation can have an infinite amount of solutions. Suppose, ax+by+c=0 and dx+ey+f=0, where x and y are variables and a≠0, b≠0, c≠0, d≠0, and e≠0.

Class 10 Maths Chapter 3 Extra Questions For Students to Practice

1. In the equation y=0, and y= -5, find the number of solutions. 

2. Find the value of (x+y) from the two equations, ax+by=a²-b², and bx+ay=0. 

3. Find if the following linear equations are inconsistent or consistent, 3x+2y=8, 6x-4y=9.

4. Draw the graph of 2x=y+3, 2y=4x-6, and check if the equation has a unique solution. 

5. Draw the equations on graph paper where the coordinates of the points intersect the lines at the y-axis. x+3y=6, 2x-3y=12. 

6. Solve x and y: 10/x+y +2/x-y =4; 15/x+y - 5/x-y =-2

7. Solve the pair of linear equations. 141x +93y =189; 93x+141y=45

8. Solve by elimination method: 3x= y+5, 5x-y=11.

9. Find the values of x and y: 27x+31y=85; 31x+27y=89

10. Find two numbers that have a sun of 75 and a difference of 15.

Benefits of CBSE Class 10 Maths Chapter 3 Important Questions

Class 10 students often face trouble with mathematics, and they often find it difficult to score good marks. With so many chapters and the number of formulas, it is impossible to remember everything. This is the reason; the set of questions help the students to revise the chapters. 

• The important question of ch 3 maths class 10 will help the students to practice last minute mathematics and revise the chapter covering all types of problems. 

• The set of important questions involve every kind of questions that might come in the exams. 

• Extra questions for class 10 maths chapter 3 is available for all the students on the Vedantu website.

Conclusion

Class 10 is a crucial year for every student, and covering all mathematics topics is important to score good grades. This set of important questions will help the students to cover all the issues and score good marks. 

Important Related Links for CBSE Class 10 Maths