Pair of Linear Equations in Two Variables
Telangana Board · Class 10 · Mathematics
Flashcards for Pair of Linear Equations in Two Variables — Telangana Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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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…
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…
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…
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…
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…
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…
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.
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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