{
  "title": "Solving by Elimination (Simultaneous Linear Equations) - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The elimination method removes one variable by: 🔄", "options": {"A": "Adding equations", "B": "Subtracting equations", "C": "Making coefficients equal then adding/subtracting", "D": "All of these"}, "correct_answer": "D"},
    {"id": 2, "difficulty": "easy", "question": "To eliminate x in 3x+2y=8 and 5x+2y=12, we: ➖", "options": {"A": "Add equations", "B": "Subtract equations", "C": "Multiply first by 5", "D": "Divide by 2"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "If coefficients of y are equal and same sign, we eliminate y by: ➕", "options": {"A": "Adding", "B": "Subtracting", "C": "Multiplying", "D": "Dividing"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "To eliminate y from 2x+3y=7 and 4x-3y=5, we: ➕", "options": {"A": "Add equations", "B": "Subtract equations", "C": "Multiply first by 2", "D": "Divide by 3"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "After eliminating one variable, we solve for: 🔢", "options": {"A": "The other variable", "B": "Both variables", "C": "Constants", "D": "Coefficients"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "If equations are x+y=5 and x-y=1, eliminating y gives: 📐", "options": {"A": "2x=6", "B": "2y=4", "C": "x=3", "D": "y=2"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "We multiply equations to make coefficients of a variable: ✖️", "options": {"A": "Equal", "B": "Different", "C": "Zero", "D": "One"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Solving 2x+3y=12 and 2x-y=4 by elimination: first step? 🚀", "options": {"A": "Subtract equations", "B": "Add equations", "C": "Multiply by 2", "D": "Divide by 2"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "If after elimination we get 0=5, system has: 🚫", "options": {"A": "Unique solution", "B": "No solution", "C": "Infinite solutions", "D": "Two solutions"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If after elimination we get 0=0, system has: ∞", "options": {"A": "Unique solution", "B": "No solution", "C": "Infinite solutions", "D": "One solution"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "To solve 3x+4y=10 and 6x+5y=20, we can multiply first equation by: 🔢", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Elimination method is also called: 📝", "options": {"A": "Substitution", "B": "Addition-subtraction method", "C": "Cross multiplication", "D": "Graphical method"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "After finding x, we find y by: 🔄", "options": {"A": "Substituting in any equation", "B": "Eliminating again", "C": "Multiplying", "D": "Dividing"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "To eliminate x from 4x+3y=9 and 2x+5y=11, multiply second by: ✖️", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "If we add equations 2x+y=7 and x-y=2, we eliminate: ➕", "options": {"A": "x", "B": "y", "C": "Both", "D": "None"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "When coefficients are opposite, elimination by adding removes the variable. Example: 3x+2y=8 and -3x+5y=10 eliminates: 🎯", "options": {"A": "x", "B": "y", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "In 5x+2y=3 and 5x-3y=7, subtracting eliminates: ➖", "options": {"A": "x", "B": "y", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "The goal of elimination is to get equation in: 🎯", "options": {"A": "One variable", "B": "Two variables", "C": "Constants", "D": "Fractions"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "If we multiply 2x+3y=6 by 3, new equation is: 🔢", "options": {"A": "6x+9y=18", "B": "6x+3y=18", "C": "2x+9y=18", "D": "6x+3y=6"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Checking solution in both original equations is called: ✅", "options": {"A": "Verification", "B": "Elimination", "C": "Substitution", "D": "Multiplication"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Solve by elimination: 5x+2y=16, 3x-2y=8. Find x. 📐", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Solve: 2x+3y=13, 4x-5y=7. Find y. 🧮", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Multiply first equation by 2: x+2y=5 becomes 2x+4y=10. To eliminate y with second equation 3x+4y=11, we: ➖", "options": {"A": "Add", "B": "Subtract", "C": "Multiply again", "D": "Divide"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "For equations 3x+4y=25, 5x-2y=9, to eliminate y, multiply second by: ✖️", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Solve: 7x-3y=15, 2x+5y=19. Find x+y. ➕", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "If 2x+3y=7 and 4x+6y=14, elimination gives: 🔄", "options": {"A": "0=0", "B": "0=7", "C": "x=1", "D": "y=2"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Solve: 0.4x+0.3y=1.7, 0.7x-0.2y=0.8. Find y. 🔢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "Equations 3x+ky=8 and 6x+12y=16 have infinite solutions if k= ? ∞", "options": {"A": "4", "B": "6", "C": "8", "D": "12"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Solve by elimination: (x/2)+(y/3)=5, (x/3)+(y/2)=6. Find x. 📐", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "If we subtract 3x+5y=12 from 5x+5y=20, we get: ➖", "options": {"A": "2x=8", "B": "2y=8", "C": "8x=32", "D": "8y=32"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Solve: 2(x+3)-3(y-2)=13, 5(x+1)+2(y-3)=10. Find y. 🔢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "For equations ax+by=c and dx+ey=f, to eliminate y we need coefficients of y to be: ⚖️", "options": {"A": "Equal", "B": "Opposite", "C": "Either equal or opposite", "D": "Zero"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Solve: 3x+2y=8, 9x-4y=2. Find x. 🧮", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "If elimination leads to 5x=15, then x=3. To find y, substitute x=3 in: 🔄", "options": {"A": "Any original equation", "B": "Only first", "C": "Only second", "D": "New equation"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Solve: 4x+7y=29, 5x+3y=22. Find y. 📐", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Equations 2x+5y=10 and 4x+10y=20 are: 🔄", "options": {"A": "Parallel", "B": "Coincident", "C": "Intersecting", "D": "Perpendicular"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Solve: 5x-4y=23, 3x+7y=4. Find x-y. ➖", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "Multiply first equation by 3 and second by 2 to eliminate y from 2x+3y=7 and 5x+2y=12. New equations: 🔢", "options": {"A": "6x+9y=21,10x+4y=24", "B": "6x+3y=21,10x+2y=24", "C": "6x+9y=7,10x+4y=12", "D": "2x+9y=21,5x+4y=24"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If 3x+4y=10 and 6x+8y=k have no solution, k ≠ ? 🚫", "options": {"A": "10", "B": "20", "C": "30", "D": "Any except 20"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Solve: 8x-3y=31, 6x+5y=11. Find x. 🧮", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "Solve by elimination: (a+b)x + (a-b)y = a²+b², (a-b)x + (a+b)y = a²-b². Find x. 📐", "options": {"A": "a", "B": "b", "C": "a+b", "D": "a-b"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "If equations 3x+2y=5 and 6x+4y=10 are multiplied to eliminate x, we multiply first by 2 and subtract, result is: 🔄", "options": {"A": "0=0", "B": "0=5", "C": "x=1", "D": "y=1"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "Solve: 2(3x+4y) = 5(2x+y), 3(x-2y) = 4(y-x). Find x/y. ➗", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "For what k do equations 4x+6y=9 and 2x+ky=6 have unique solution? ✅", "options": {"A": "k ≠ 3", "B": "k = 3", "C": "k ≠ 4", "D": "k = 4"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "Solve: 0.2x + 0.5y = 0.7, 0.3x + 0.4y = 0.8. Multiply by 10 first: 🧮", "options": {"A": "2x+5y=7, 3x+4y=8", "B": "20x+50y=70, 30x+40y=80", "C": "0.2x+0.5y=7, 0.3x+0.4y=8", "D": "x+y=7, x+y=8"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Equations (k+2)x + 5y = 7, 3x + (k+3)y = 10 have no solution if k = ? 🚫", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "Solve: (x+y)/3 + (x-y)/2 = 4, (x+y)/2 - (x-y)/3 = 1. Find x. 🔢", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "If we add equations ax+by=c and bx+ay=d, we get (a+b)(x+y)=c+d. Useful if we want: ➕", "options": {"A": "x+y", "B": "x-y", "C": "xy", "D": "x/y"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "Solve: 3/x + 2/y = 7, 5/x - 4/y = 6. Let u=1/x, v=1/y. Find y. 🔄", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "1/5"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "For equations 2x+3y=7, 4x+ky=14 to have infinite solutions, k= ? ∞", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "Solve: a(x+y) + b(x-y) = a²+b², a(x-y) + b(x+y) = a²-b². Find x. 📐", "options": {"A": "a", "B": "b", "C": "a+b", "D": "a-b"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "Elimination applied to 5x+2y=3 and 10x+4y=6 yields: 🔄", "options": {"A": "0=0", "B": "0=3", "C": "x=1", "D": "y=1"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "Solve: 0.3x - 0.4y = 0.1, 0.5x + 0.2y = 0.7. Find x+y. ➕", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "hard", "question": "If subtracting 2*(first eq) from second eq eliminates x in 3x+4y=10 and 6x+5y=20, then second eq multiplied? ✖️", "options": {"A": "No need", "B": "Multiply first by 2", "C": "Multiply second by 2", "D": "Multiply both by 2"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "Solve: (2x+1)/5 + (3y-2)/4 = 2, (3x+1)/2 - (y+2)/3 = 1. Find y. 🧮", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "For equations px+3y=9, 4x+py=12 to be inconsistent, p must satisfy: 🚫", "options": {"A": "p²=12", "B": "p=±√12", "C": "p=√12 only", "D": "p=-√12 only"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "Solve: 6x+5y=7x+3y+1=2(x+6y-1). Rearrange to two equations. Find x. 🔢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "If we add equations 3x+4y=5 and 5x-4y=3, y is eliminated. Then x= ? 📐", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "Solve: (x+1)/2 + (y-1)/3 = 4, (x-1)/3 + (y+1)/2 = 4. Find x*y. ✖️", "options": {"A": "12", "B": "15", "C": "18", "D": "20"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "hard", "question": "Equations (k-1)x+3y=5, 4x+6y=10 have infinite solutions when k= ? ∞", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"}
  ]
}