Pair of Linear Equations in Two Variables — Flashcards
Gujarat Board · Class 10 · Mathematics
25 flashcards for Pair of Linear Equations in Two Variables (Gujarat Board Class 10 Mathematics) to test yourself on key terms and facts.
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Solve the pair of equations using substitution method: y = 2x + 1 3x + y = 11
Answer
Step 1: We have y = 2x + 1 from the first equation. Step 2: Substitute this value of y into the second equation: 3x + (2x + 1) = 11 Step 3: Simplify: 5x + 1 = 11 Step 4: Solve for x: 5x = 10 → x = 2 S…
Solve using the elimination method: 2x + 3y = 13 5x - 3y = 8
Answer
Step 1: Observe that the coefficients of y are +3 and -3 (opposites). Step 2: Add both equations to eliminate y: (2x + 3y) + (5x - 3y) = 13 + 8 Step 3: Simplify: 7x = 21 Step 4: Solve for x: x = 3 Ste…
Determine if the pair of equations is consistent, inconsistent, or dependent: 3x + 4y = 12 6x + 8y = 24
Answer
For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, rewrite: 3x + 4y - 12 = 0 6x + 8y - 24 = 0 Calculate the ratios: a₁/a₂ = 3/6 = 1/2 b₁/b₂ = 4/8 = 1/2 c₁/c₂ = -12/-24 = 1/2 Since a₁/a₂ = b₁/b…
Check whether the lines represented by these equations are intersecting, parallel, or coincident: x + 2y = 4 2x + 4y = 12
Answer
Rewrite in standard form: x + 2y - 4 = 0 2x + 4y - 12 = 0 Calculate the ratios: a₁/a₂ = 1/2 b₁/b₂ = 2/4 = 1/2 c₁/c₂ = -4/-12 = 1/3 Observation: a₁/a₂ = b₁/b₂ ≠ c₁/c₂ (since 1/2 ≠ 1/3) Answer: The l…
Solve the pair of equations: 2x + y = 7 x - y = 2
Answer
Using the elimination method (y coefficients are opposite: +1 and -1): Step 1: Add both equations: (2x + y) + (x - y) = 7 + 2 Step 2: Simplify: 3x = 9 Step 3: Solve for x: x = 3 Step 4: Substitute x …
Akhila spent ₹20 at a fair. She had rides on a Giant Wheel (₹3 each) and played Hoopla (₹4 each). The number of Hoopla games is half the number of rides. Find how many rides and games she had.
Answer
Step 1: Define variables Let x = number of rides on Giant Wheel Let y = number of Hoopla games Step 2: Set up equations from the given information Equation 1 (money spent): 3x + 4y = 20 Equation 2 (r…
Solve by elimination method with multiplication: 3x + 2y = 8 2x + 3y = 7
Answer
Step 1: Observe that no coefficients are directly opposite. We need to multiply to make them so. Step 2: To eliminate x, multiply first equation by 2 and second by 3: First equation × 2: 6x + 4y = 16 …
When do you use the graphical method to solve a pair of linear equations? What are its advantages and limitations?
Answer
The graphical method involves plotting both equations as lines on a coordinate plane. When to use it: • When you want to visualize the relationship between the equations • When the solution values ar…
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