Easy Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the general form of a pair of linear equations in two variables.
(2) Solve the pair of equations: x + y = 7, x - y = 3. x =
Correct! Adding the equations: 2x = 10, so x = 5. Substituting: y = 7 - 5 = 2.
(3) Find whether the pair x + 2y = 6 and 2x + 4y = 12 is consistent or inconsistent.
Perfect! The second equation is 2 times the first, so they represent the same line.
(4) Find the value of k, if the equations 3x + ky = 9 and 6x + 4y = 18 have a unique solution. k
Excellent! For unique solution:
(5) How many solutions does the pair 2x - 3y = 6, 4x - 6y = 12 have?
Correct! The equations are equivalent (second is 2 times the first), so infinitely many solutions.
Short Answer Questions (2 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Solve the pair of equations: x + y = 5, 2x - y = 4. x =
Perfect! Adding equations: 3x = 9, so x = 3. Then y = 5 - 3 = 2.
(2) Find the solution of the pair 3x + 2y = 12, x - y = 1 by substitution method. x =
Excellent! From x - y = 1, we get x = y + 1. Substituting: 3(y + 1) + 2y = 12, giving y = 3, x = 2.
(3) A number consists of two digits whose sum is 9. If the digits are reversed, the number is increased by 27. Find the number. The number is
Perfect! Let the number be 10x + y. Then x + y = 9 and (10y + x) - (10x + y) = 27, solving gives x = 3, y = 6.
(4) Check whether the pair: x - y = 4 and 2x - 2y = 9 has a solution.
Correct! The ratios
(6) Draw the graph of the equation x + y = 6 and find the coordinates where the line intersects the axes. x-intercept:
Excellent! When y = 0, x = 6 and when x = 0, y = 6.
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Solve the following pair using the graphical method: 2x + y = 7, x - y = 1. x =
(2) The sum of a two-digit number and the number obtained by reversing its digits is 99. If the digits differ by 3, find the number. The numbers are
Perfect! Let the digits be x and y. Then (10x + y) + (10y + x) = 99 and |x - y| = 3, giving solutions 36 and 63.
(3) Solve the equations: 3x + 4y = 10, 2x - y = 1 using the elimination method. x =
Excellent! Multiplying second equation by 4: 8x - 4y = 4. Adding: 11x = 14, so x = 2, y = 1.
(4) The father's age is three times the son's age. After five years, the father's age will be two times the son's age. Find their present ages. Father:
Perfect! Let son's age = x, father's age = 3x. After 5 years: 3x + 5 = 2(x + 5), solving gives x = 10.
(5) Solve: 0.2x + 0.3y = 1.3, 0.4x + 0.5y = 2.3. x =
Excellent! Multiplying by 10: 2x + 3y = 13, 4x + 5y = 23. Solving gives x = 2, y = 3.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The pair of equations x + y = 10 and x - y = 2 is
(a) Consistent and independent (b) Inconsistent (c) Consistent and dependent (d) No solution
Correct! The equations have different slopes, so they intersect at exactly one point.
(2) The solution of 2x + y = 8, x - y = 1 is
(a) (3, 2) (b) (2, 4) (c) (4, 0) (d) (2, 3)
Correct! Adding the equations: 3x = 9, so x = 3. Then y = 8 - 6 = 2.
(3) If a pair of linear equations has infinitely many solutions, they are
(a) Parallel lines (b) Intersecting lines (c) Coincident lines (d) Perpendicular lines
Correct! Coincident lines are the same line, hence infinitely many common points.
(4) Which of the following is the general form of a linear equation in two variables?
(a)
Correct! This is the general form where both variables have degree 1.
(5) The graph of a pair of equations intersecting at a point represents
(a) No solution (b) Infinite solutions (c) Unique solution (d) Cannot be determined
Correct! One point of intersection means exactly one solution.
(6) If
(a) No solution (b) A unique solution (c) Infinitely many solutions (d) Can't say
Correct! Different slopes mean the lines intersect at exactly one point.
(7) The graphical representation of an inconsistent pair of equations is
(a) Intersecting lines (b) Parallel lines (c) Coincident lines (d) Curves
Correct! Parallel lines never meet, representing no solution.
(8) The pair 4x + 5y = 20 and 8x + 10y = 40 has
(a) No solution (b) Unique solution (c) Infinitely many solutions (d) Can't say
Correct! The second equation is exactly 2 times the first, so they're the same line.
(9) The solution of x = 3, y = 2 satisfies which pair?
(a) x + y = 5, x - y = 1 (b) x + y = 6, x - y = 1 (c) x + y = 7, x - y = 1 (d) x + y = 7, x - y = 0
Correct! Substituting x = 3, y = 2: 3 + 2 = 5 and 3 - 2 = 1.
(10) Which of the following methods is not used to solve a pair of linear equations?
(a) Elimination method (b) Graphical method (c) Substitution method (d) Factorisation method
Correct! Factorization is used for quadratic equations, not linear systems.
Linear Equations Challenge
Determine whether these statements about linear equations are True or False: