{
  "title": "Solving by Substitution (Simultaneous Linear Equations) - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "In substitution method, we first express one variable in terms of: 🔤", "options": {"A": "The other variable", "B": "Constants", "C": "Coefficients", "D": "Both variables"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "From x + y = 5, we can write x = ? ➖", "options": {"A": "5 + y", "B": "5 - y", "C": "y - 5", "D": "y/5"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "After expressing x in terms of y, we substitute into: 🔄", "options": {"A": "The same equation", "B": "The other equation", "C": "Both equations", "D": "Any equation"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Substitution is useful when one variable has coefficient: 🔢", "options": {"A": "Zero", "B": "One", "C": "Fraction", "D": "Any number"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "If y = 3x + 2 from first equation, we substitute y in second equation to get equation in: 📐", "options": {"A": "x only", "B": "y only", "C": "Both x and y", "D": "Constants"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "After solving for one variable, we find the other by: 🔄", "options": {"A": "Substituting back", "B": "Solving new equation", "C": "Elimination", "D": "Cross multiplication"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "From 2x - y = 3, we can write y = ? 📝", "options": {"A": "2x - 3", "B": "3 - 2x", "C": "2x + 3", "D": "3 + 2x"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "The substitution method is also called: 🏷️", "options": {"A": "Elimination method", "B": "Comparison method", "C": "Trial and error", "D": "Graphical method"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "If x = 4 from first equation, substitute in second to find: 🔍", "options": {"A": "y", "B": "x again", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "For equations x = 2y and 3x + y = 14, substituting x gives: 🔄", "options": {"A": "3(2y) + y = 14", "B": "2y + y = 14", "C": "3x + 2y = 14", "D": "x + y = 14"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "If substitution leads to 5 = 5, system has: ∞", "options": {"A": "No solution", "B": "Unique solution", "C": "Infinite solutions", "D": "Two solutions"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "If substitution leads to 3 = 7, system has: 🚫", "options": {"A": "No solution", "B": "Unique solution", "C": "Infinite solutions", "D": "One solution"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "From y = 2x + 1, substituting into 3x + 2y = 11 gives: 🔢", "options": {"A": "3x + 2(2x+1) = 11", "B": "3x + 2x+1 = 11", "C": "3(2x+1) + 2y = 11", "D": "3x + 2 = 11"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "In substitution, we solve for the variable with coefficient 1 to avoid: ➗", "options": {"A": "Fractions", "B": "Decimals", "C": "Large numbers", "D": "All of these"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "After finding x = 3, we substitute into y = 2x - 1 to get y = ? 🧮", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "We can express variable from any equation but choose the one that gives: ✅", "options": {"A": "Simple expression", "B": "Complex expression", "C": "No expression", "D": "Zero"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "If equations are x = 5 and 2x + y = 12, then y = ? 🔢", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Substitution works best when one equation is already solved for: 🎯", "options": {"A": "One variable", "B": "Both variables", "C": "Constants", "D": "Coefficients"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Checking solution means plugging values into: 🔍", "options": {"A": "Original equations", "B": "Modified equations", "C": "One equation", "D": "No equation"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "From 3x + y = 10, we can write y = ? 📝", "options": {"A": "10 - 3x", "B": "3x - 10", "C": "10 + 3x", "D": "3x + 10"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Solve by substitution: x + y = 7, 2x - 3y = 9. Find x. 📐", "options": {"A": "6", "B": "5", "C": "4", "D": "3"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Solve: y = 2x - 1, 3x + 4y = 23. Find y. 🧮", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "From 3x - 2y = 8, express x in terms of y: 🔄", "options": {"A": "x = (8+2y)/3", "B": "x = (8-2y)/3", "C": "x = (2y-8)/3", "D": "x = 8+2y/3"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Solve: 5x + 2y = 11, x - y = 1. Find x. 🔢", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "If x = 3y + 4 from first equation and second is 2x + 5y = 3, substituting gives: 🔄", "options": {"A": "2(3y+4)+5y=3", "B": "3y+4+5y=3", "C": "2(3y)+5y=3", "D": "2(4)+5y=3"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Solve: 0.2x + 0.3y = 1.4, 0.4x - 0.5y = 1.0. Express y from first: 📝", "options": {"A": "y = (1.4-0.2x)/0.3", "B": "y = (0.2x-1.4)/0.3", "C": "y = 1.4-0.2x", "D": "y = 0.3x+1.4"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Solve: (x/2) + (y/3) = 5, (x/3) - (y/2) = 1. Express x from first? 🔢", "options": {"A": "x = 10 - (2y/3)", "B": "x = 5 - (y/3)", "C": "x = 10 - (y/3)", "D": "x = 5 - (2y/3)"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "For equations 4x + y = 9 and 3x + 2y = 8, substitution after expressing y = 9-4x gives: 🔄", "options": {"A": "3x+2(9-4x)=8", "B": "4(9-4x)+y=9", "C": "3x+2y=9-4x", "D": "None"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Solve: 2x + 3y = 13, 4x - y = 5. Find y. 🧮", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "If substituting leads to 7x = 21, then x = 3. Then find y from y = 2x + 1: 🔄", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Solve: 3(x+2) + 2(y-1) = 20, 2(x-1) + 3(y+2) = 25. Express x from first? 📐", "options": {"A": "x = (20-2(y-1))/3 - 2", "B": "x = (20-2y+2)/3 - 2", "C": "x = (22-2y)/3 - 2", "D": "All of these"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "For equations 5x - 3y = 1, 2x + y = 9, substitute y = 9-2x into first gives: 🔄", "options": {"A": "5x-3(9-2x)=1", "B": "5x-3(2x+9)=1", "C": "5x-3(2x-9)=1", "D": "5x-3(9)=1"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Solve: 7x - 4y = 15, 5x + y = 12. Find x. 🧮", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If substitution gives 0 = 0, system is: ∞", "options": {"A": "Inconsistent", "B": "Consistent, unique", "C": "Consistent, infinite", "D": "Dependent and consistent"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "Solve: x = 2y - 1, 3x - 4y = 7. Find y. 🔢", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "From 1.5x + 2y = 8, express y = ? 📝", "options": {"A": "y = (8-1.5x)/2", "B": "y = 8-1.5x", "C": "y = 1.5x-8", "D": "y = (1.5x-8)/2"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Solve: (x+1)/2 + (y-1)/3 = 4, (x-2)/3 + (y+1)/2 = 5. Express x from first? 🧮", "options": {"A": "x = 8 - 2(y-1)/3 - 1", "B": "x = 8 - 2(y-1)/3", "C": "x = 8 - (y-1)/3", "D": "x = 4 - (y-1)/3"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "If y = 4x - 3 and 2x + 3y = 41, then x = ? 📐", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Solve: 6x + 5y = 7x + 3y + 1, 2x - y = x + 2y - 3. Find x+y. ➕", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "For equations ax+by=c and dx+ey=f, substitution works well if |a|=1 or |b|=1 because: ✅", "options": {"A": "Easy to isolate variable", "B": "No fractions", "C": "Simpler arithmetic", "D": "All of these"}, "correct_answer": "D"},
    {"id": 41, "difficulty": "hard", "question": "Solve by substitution: (a+b)x + (a-b)y = a²+b², (a-b)x + (a+b)y = a²-b². Find y. 📐", "options": {"A": "b", "B": "a", "C": "a+b", "D": "a-b"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "If x = (3y+1)/2 from first equation and second is 5x - 4y = 8, substituting gives: 🔄", "options": {"A": "5(3y+1)/2 - 4y = 8", "B": "(3y+1)/2 - 4y = 8", "C": "5(3y+1) - 4y = 8", "D": "5(3y+1)/2 = 8"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "Solve: 2/x + 3/y = 7, 5/x - 4/y = 6. Let 1/x = p, 1/y = q. Find y. 🔢", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "1/5"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "For equations 3x + 4y = 10 and 6x + 8y = k to have infinite solutions, substitution leads to identity if k = ? ∞", "options": {"A": "20", "B": "15", "C": "10", "D": "5"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "Solve: 0.3x - 0.4y = 0.1, 0.5x + 0.2y = 0.7. Multiply by 10 first, then substitute. Find x. 🧮", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "If substituting gives 5y = 10, then y = 2. Then x = 3y - 5 gives x = ? 🔢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "Solve: (x+y)/a + (x-y)/b = 2, (x+y)/b - (x-y)/a = 0. Let u=x+y, v=x-y. Find x. 📐", "options": {"A": "a", "B": "b", "C": "a+b", "D": "a-b"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "For equations 2x + py = 8, 4x + 2y = q to be inconsistent, substitution leads to contradiction if: 🚫", "options": {"A": "p=4, q≠16", "B": "p=2, q≠8", "C": "p=1, q≠4", "D": "p=3, q≠12"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "Solve: 3(x+2y) + 4(2x-y) = 5, 5(x+2y) - 2(2x-y) = 3. Let a=x+2y, b=2x-y. Find y. 🔢", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "1/5"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "If from first equation x = (5-3y)/2 and substituting into second gives 4((5-3y)/2) + 5y = 11, simplify: 🔄", "options": {"A": "10-6y+5y=11", "B": "20-12y+5y=11", "C": "10-12y+5y=11", "D": "10-3y+5y=11"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "Solve: ax + by = a²+b², bx + ay = 2ab. Find x if a≠b. 📐", "options": {"A": "a", "B": "b", "C": "a+b", "D": "a-b"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "hard", "question": "Substitution in 2x+3y=7 and 4x+6y=14 gives: 🔄", "options": {"A": "Identity", "B": "Contradiction", "C": "x=1", "D": "y=1"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "Solve: 1/(x+y) + 2/(x-y) = 2, 3/(x+y) - 1/(x-y) = 1. Let u=1/(x+y), v=1/(x-y). Find x. 🧮", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "If y = mx + c from first eq and second is px + qy = r, substitution yields equation in x only if: 📝", "options": {"A": "Always", "B": "Never", "C": "Only if m,p,q known", "D": "Only if c=0"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "Solve: (2x+3y)/4 = (3x+4y)/5 = 1. Take first two equal, then first=1. Find y. 🔢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "For equations (k+1)x + 5y = 7, 3x + (k+3)y = 10 to have no solution, substitution leads to impossible equation if k = ? 🚫", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "hard", "question": "Solve: 0.2x + 0.5y = 0.7, 0.3x + 0.4y = 0.8. Express y from first, substitute. Find x+y. ➕", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "If x = 2y - 3 and 3x - 4y = 5, then y = ? 📐", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "Solve: (x+1)/3 - (y-2)/4 = 1, (x-2)/2 + (y+1)/5 = 3. Express x from first? 🧮", "options": {"A": "x = 3 + 3(y-2)/4 - 1", "B": "x = 3 + 3(y-2)/4", "C": "x = 3 + (y-2)/4 - 1", "D": "x = 3 + (y-2)/4"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "If substitution gives 4 = 4, then system has: ∞", "options": {"A": "No solution", "B": "Unique solution", "C": "Infinite solutions", "D": "Two solutions"}, "correct_answer": "C"}
  ]
}