Pair of Linear Equations in Two Variables
Punjab Board · Class 10 · Mathematics
Flashcards for Pair of Linear Equations in Two Variables — Punjab Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedSolve by substitution method: x + y = 10 and x - y = 2
Answer
Step 1: From first equation, express x in terms of y: x = 10 - y Step 2: Substitute in second equation: (10 - y) - y = 2 Step 3: Simplify: 10 - 2y = 2 Step 4: Solve for y: 2y = 8, so y = 4 Step 5: Sub…
Solve by elimination method: 2x + 3y = 13 and 3x - 2y = 4
Answer
Step 1: Multiply first equation by 2: 4x + 6y = 26 Step 2: Multiply second equation by 3: 9x - 6y = 12 Step 3: Add equations to eliminate y: (4x + 9x) + (6y - 6y) = 26 + 12 Step 4: Simplify: 13x = 38,…
When should you use the substitution method instead of elimination method?
Answer
Use substitution method when: 1. One equation is already solved for one variable (like y = 2x + 5) 2. One variable has coefficient 1 or -1 (easy to isolate) 3. Coefficients are small and don't need mu…
Determine the nature of lines: Compare ratios a₁/a₂, b₁/b₂, c₁/c₂ for equations: 2x + 3y = 7 and 4x + 6y = 15
Answer
For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 Given: 2x + 3y - 7 = 0 and 4x + 6y - 15 = 0 Step 1: Calculate ratios: a₁/a₂ = 2/4 = 1/2 b₁/b₂ = 3/6 = 1/2 c₁/c₂ = -7/-15 = 7/15 Step 2: Compare …
Solve the system: 7x - 15y = 2 and x + 2y = 3
Answer
Using Substitution Method: Step 1: From second equation, isolate x: x = 3 - 2y Step 2: Substitute in first equation: 7(3 - 2y) - 15y = 2 Step 3: Expand: 21 - 14y - 15y = 2 Step 4: Combine like terms: …
Akhila spent ₹20 total. Rides on Giant Wheel cost ₹3 each, Hoopla costs ₹4 per game. She played Hoopla half as many times as rides. Find number of rides and games.
Answer
Step 1: Define variables. Let x = number of rides, y = number of Hoopla games Step 2: Form equations: Condition 1: y = x/2 (Hoopla times = half the rides) Condition 2: 3x + 4y = 20 (total cost) Step 3…
Check if this pair has infinitely many solutions: 5x - 8y + 1 = 0 and 10x - 16y + 2 = 0
Answer
Step 1: Compare coefficients. Rewrite second equation by dividing by 2: 5x - 8y + 1 = 0 Step 2: Notice that both equations become identical when second is divided by 2. Step 3: Check ratios: a₁/a₂ = 5…
Solve by elimination: 3x + 4y = 10 and 2x - 2y = 2
Answer
Step 1: Make coefficients of y equal. Multiply first equation by 1 and second by 2: 3x + 4y = 10 4x - 4y = 4 Step 2: Add equations to eliminate y: (3x + 4x) + (4y - 4y) = 10 + 4 7x = 14 x = 2 Step 3: …
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