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Pair of Linear Equations in Two Variables — Flashcards

Telangana Board · Class 10 · Mathematics

30 flashcards for Pair of Linear Equations in Two Variables (Telangana Board Class 10 Mathematics) to test yourself on key terms and facts.

43 questions30 flashcards9 formulas & key relations5 concepts

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30 Flashcards·
Solving a pair of equationsNeed for two equationsLinear equation formElimination methodNature of pair of equations
Card 1Solving a pair of equations

Solve using the model idea: Siri bought 3 notebooks and 2 pens for ₹80. Laxmi bought 4 notebooks and 3 pens for ₹110. Find the cost of one notebook and one pen.

Answer

Let the cost of one notebook be x and one pen be y. Step 1: Form equations 3x + 2y = 80 4x + 3y = 110 Step 2: Eliminate one variable Multiply the first equation by 3: 9x + 6y = 240 Multiply the seco…

Card 2Need for two equations

Why are two equations needed for two unknowns?

Answer

One equation with two unknowns has many solutions. Example: x + y = 10 Possible pairs include (0,10), (1,9), (2,8), and so on. Step 1: One equation gives only a relationship. Step 2: A second indepe…

Card 3Linear equation form

Formula for a linear equation in two variables

Answer

General form: ax + by + c = 0, where a² + b² ≠ 0 Here: - x and y are variables - a, b, c are real numbers - at least one of a or b must be non-zero Quick example: 2x + 3y - 5 = 0 is linear because x…

Card 4Elimination method

Solve: 2x + y - 5 = 0 and 3x - 2y - 4 = 0

Answer

Step 1: Write in standard form 2x + y = 5 3x - 2y = 4 Step 2: Eliminate y Multiply first equation by 2: 4x + 2y = 10 Add with second equation: (4x + 2y) + (3x - 2y) = 10 + 4 7x = 14 x = 2 Step 3: S…

Card 5Nature of pair of equations

What kind of lines do 3x + 4y = 2 and 6x + 8y = 4 represent?

Answer

Step 1: Compare ratios 3/6 = 1/2 4/8 = 1/2 -2/-4 = 1/2 Step 2: Since a1/a2 = b1/b2 = c1/c2, the lines are coincident. Step 3: Coincident lines have infinitely many solutions. Answer: Consistent and…

Card 6Nature of pair of equations

What kind of lines do 2x - 3y = 5 and 4x - 6y = 15 represent?

Answer

Step 1: Compare ratios 2/4 = 1/2 -3/-6 = 1/2 -5/-15 = 1/3 Step 2: Since a1/a2 = b1/b2 ≠ c1/c2, the lines are parallel. Step 3: Parallel lines never meet, so there is no solution. Answer: Inconsiste…

Card 7Nature of pair of equations

What kind of lines do 3x + 2y - 80 = 0 and 4x + 3y - 110 = 0 represent?

Answer

Step 1: Compare ratios 3/4 ≠ 2/3 Step 2: Since a1/a2 ≠ b1/b2, the lines intersect. Step 3: Intersecting lines have one unique solution. Answer: Consistent and independent; one solution.

Card 8Elimination method

Solve: 3x + 2y = 11 and 2x + 3y = 4

Answer

Step 1: Eliminate y Multiply first equation by 3: 9x + 6y = 33 Multiply second equation by 2: 4x + 6y = 8 Step 2: Subtract 9x + 6y - (4x + 6y) = 33 - 8 5x = 25 x = 5 Step 3: Substitute x = 5 in 3x +…

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Frequently Asked Questions

What are the important topics in Pair of Linear Equations in Two Variables for Telangana Board Class 10 Mathematics?
Key topics in Pair of Linear Equations in Two Variables include Basic Ideas and Definitions, Formation of Equations from Word Problems, Graphical Method and Nature of Solutions, Algebraic Methods: Substitution and Elimination. Study these first, then practise questions on each for the Telangana Board Class 10 board exam.
How many flashcards are available for Pair of Linear Equations in Two Variables?
There are 30 flashcards for Pair of Linear Equations in Two Variables covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Pair of Linear Equations in Two Variables for the Telangana Board Class 10 board exam?
Learn the core ideas first, then work through the 43 practice questions on Pair of Linear Equations in Two Variables. Revise definitions regularly and use flashcards for quick recall before the exam.

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