Easy Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Define a linear equation in two variables. An equation of the form
Perfect! A linear equation in two variables has degree 1 for each variable.
(2) Give one example of a linear equation in two variables.
Excellent! This is a simple linear equation with two variables.
(3) How many solutions does a linear equation in two variables have?
Correct! Each linear equation represents a line with infinite points.
(5) Write whether x + y = 5 is a linear equation in two variables.
Perfect! It is a linear equation in two variables. It has degree 1 in both x and y.
Short Answer Questions (2 Marks Each)
Answer each question with complete working
(1) Write the solution set of x + y = 6 when x = 2, 3, 4.
Solution set:
Excellent! These are three solutions to the equation.
(2) Verify whether (1, 2) is a solution of 2x + 3y = 8.
Perfect verification!
(3) If x = 2, find y from the equation 3x + 2y = 12. y =
Great! When x = 2, y = 3.
(4) Write the coordinates of two points satisfying x - y = 4.
Point 1:
Point 2:
Excellent! Any two points on the line work.
(5) Draw the graph of the equation x + y = 4 for two points.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete graph plotting and detailed steps. Write down the answers on sheet and submit to the school subject teacher.
(1) Draw the graph of the equation 2x + y = 6 by finding at least three solutions.
Solution 1:
Solution 2:
Solution 3:
(2) Draw the graph of the equation x - y = 2 by taking x = 0, 2, 4.
(3) Plot the graph of 3x + 2y = 12 and find the points where the graph cuts the x-axis and y-axis.
x-intercept (y = 0):
y-intercept (x = 0):
The line cuts x-axis at (4, 0) and y-axis at (0, 6).
(4) Draw the graph of the linear equation x + 2y = 8 and write any two solutions.
Solution 1:
Solution 2:
Any such points are valid solutions.
(5) Draw the graph of y = 2x + 1 by taking suitable values of x.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The general form of a linear equation in two variables is:
(a) ax + by + c = 0 (b)
Correct! This is the standard form of a linear equation in two variables.
(2) A linear equation in two variables represents:
(a) A point (b) A line (c) A curve (d) A parabola
Correct! Linear equations always represent straight lines.
(3) The equation 2x + 3y = 12 is satisfied by:
(a) (2, 3) (b) (3, 2) (c) (0, 4) (d) (4, 0)
Correct! 2(3) + 3(2) = 6 + 6 = 12.
(4) The equation x + y = 5 has:
(a) No solution (b) One solution (c) Infinitely many solutions (d) Two solutions
Correct! Linear equations have infinitely many solutions (all points on the line).
(5) The graph of a linear equation in two variables is always:
(a) A straight line (b) A curve (c) A point (d) None
Correct! Linear equations always produce straight line graphs.
(6) Which of the following is not a linear equation in two variables?
(a) x + y = 3 (b) x - y = 7 (c) xy = 2 (d) 2x + 3y = 5
Correct! xy = 2 is quadratic (product of variables), not linear.
(7) In the equation 3x + 2y = 12, the coefficient of y is:
(a) 3 (b) 2 (c) 12 (d) 0
Correct! The coefficient of y in 3x + 2y = 12 is 2.
(8) The x-intercept of 2x + y = 6 is:
(a) 0 (b) 2 (c) 3 (d) 6
Correct! When y = 0: 2x + 0 = 6, so x = 3.
(9) The y-intercept of x + y = 4 is:
(a) 0 (b) 4 (c) 2 (d) -4
Correct! When x = 0: 0 + y = 4, so y = 4.
(10) Which of the following points lies on the line x - y = 2?
(a) (2, 2) (b) (3, 1) (c) (4, 2) (d) (5, 2)
Correct! For (3, 1): 3 - 1 = 2.
Let's classify different types of equations!!!
Excellent! Linear equations have degree 1 in each variable.
True or False: Solution Verification
Check if these points satisfy their given equations: