Class 10 Maths - WEST-BENGAL
Pair of Linear Equations in Two Variables
In this chapter, Class 10 students under the West Bengal Board of Secondary Education (WBBSE) learn to solve two linear equations simultaneously in two variables, such as x and y. You will explore algebraic methods like substitution, elimination, and cross-multiplication, alongside graphical representations to understand consistent, inconsistent, and dependent systems. This chapter is vital for board exams as it frequently features 3-mark and 5-mark word problems that test your ability to translate real-life scenarios into mathematical equations.
Start Learning FreeKey Concepts
Linear Equation in Two Variables
An equation of the form ax + by + c = 0, where a, b, and c are real numbers and a, b are not both zero, representing a straight line on a graph.
Consistent System
A pair of linear equations that has at least one solution, which includes intersecting lines (unique solution) and coincident lines (infinitely many solutions).
Inconsistent System
A pair of linear equations that has no solution at all, represented graphically by parallel lines that never intersect.
Method of Elimination
An algebraic technique where one variable is eliminated by adding or subtracting the equations after making its coefficients equal.
Method of Substitution
An algebraic approach where the value of one variable from one equation is expressed in terms of the other and substituted into the second equation.
Important Formulas
Board Exam Info
In the WBBSE Madhyamik examination, this chapter usually carries around 8 to 10 marks. Common question types include checking consistency using ratio comparisons, solving algebraic simultaneous equations using elimination or cross-multiplication, and solving crucial 5-mark word problems based on age, speed-distance, or fractions.
Frequently Asked Questions
How do I know if a pair of linear equations has a unique solution?
You compare the ratios of the coefficients. If a1/a2 is not equal to b1/b2, the system has a unique solution and the lines intersect at only one point.
Can I use any method to solve simultaneous equations in the board exam?
Yes, unless the question specifically asks you to use a particular method like cross-multiplication or graphical method, you can use elimination or substitution as per your convenience.
What should I do if the graph lines are parallel?
If the lines are parallel, state clearly that the equations are inconsistent and have no solution.
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