Linear Equations
NIOS · Class 10 · Maths
Flashcards for Linear Equations — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allSolve: 2x + 7 = 15
Answer
Step 1: Subtract 7 from both sides → 2x + 7 - 7 = 15 - 7 → 2x = 8 Step 2: Divide both sides by 2 → x = 8/2 = 4 Verification: 2(4) + 7 = 8 + 7 = 15 ✓ Answer: x = 4…
Solve: 3(x - 4) = 2x + 5
Answer
Step 1: Expand the left side → 3x - 12 = 2x + 5 Step 2: Subtract 2x from both sides → 3x - 2x - 12 = 5 → x - 12 = 5 Step 3: Add 12 to both sides → x = 5 + 12 = 17 Verification: 3(17 - 4) = 3(13) = 39 …
Solve: (x + 2)/3 - (x - 1)/2 = 1
Answer
Step 1: Find LCM of 3 and 2 = 6 Step 2: Multiply entire equation by 6 → 2(x + 2) - 3(x - 1) = 6 Step 3: Expand → 2x + 4 - 3x + 3 = 6 Step 4: Simplify → -x + 7 = 6 → -x = -1 → x = 1 Verification: (1+2)…
Find three solutions of 2x + 3y = 12
Answer
Method: Choose values for x, then find y Solution 1: x = 0 → 2(0) + 3y = 12 → y = 4 → (0, 4) Solution 2: x = 3 → 2(3) + 3y = 12 → 6 + 3y = 12 → y = 2 → (3, 2) Solution 3: x = 6 → 2(6) + 3y = 12 → 12 +…
Solve graphically: x + y = 5 and x - y = 1
Answer
For x + y = 5: Points (0,5), (5,0), (2,3) For x - y = 1: Points (0,-1), (1,0), (3,2) Step 1: Plot both lines on graph paper Step 2: Find intersection point by observation Intersection point: (3, 2) Ve…
Solve by substitution: x + 2y = 7 and 3x - y = 4
Answer
Step 1: From first equation → x = 7 - 2y Step 2: Substitute in second equation → 3(7 - 2y) - y = 4 Step 3: Expand → 21 - 6y - y = 4 → 21 - 7y = 4 Step 4: Solve for y → -7y = -17 → y = 17/7 Step 5: Fin…
Solve by elimination: 2x + 3y = 11 and 4x - 2y = 2
Answer
Step 1: To eliminate x, multiply first equation by 2 → 4x + 6y = 22 Step 2: Subtract second from new first → (4x + 6y) - (4x - 2y) = 22 - 2 Step 3: Simplify → 8y = 20 → y = 2.5 Step 4: Substitute y = …
A number increased by 15 equals 3 times the number. Find the number.
Answer
Step 1: Let the number be x Step 2: According to problem → x + 15 = 3x Step 3: Rearrange → 15 = 3x - x → 15 = 2x Step 4: Solve → x = 15/2 = 7.5 Verification: 7.5 + 15 = 22.5 and 3 × 7.5 = 22.5 ✓ Answe…
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