CONDITIONS FOR GRAPHICAL REPRESENTATION AND ALGEBRAIC INTERPRETATION PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 03 Class 10th Mathematics (Practice Sheet) 1 Which of the following is the algebraic representation of the equation 2x - y = -1? A. x - y = 1 B. x + 2y = 0 C. 2x - y + 1 = 0 D. 2x - y = 0 2 What do the points A(0, 0) and B(2, 1) represent on a graph in the context of linear equations? A. Intersection points B. Solutions to x - 2y = 0 C. Parallel lines D. Coinciding lines 3 In the geometric representation of linear equations, when two lines are parallel, what does it indicate about the equations? A. They have no solutions B. They intersect at a single point C. They have infinitely many solutions D. They are inconsistent 4 Which of the following is the geometric representation of the equation 3x + 4y = 20? A. A single point B. A straight line connecting points P(0, 5) and Q(4, 2) C. No intersection D. Parallel lines 5 What is the algebraic representation of the equation 2x - 3y = 6? A. 2x - 3y = 0 B. 2x + 3y = 6 C. 2x - 3y = 6 D. 2x = 3y + 6 6 Solve the system by graphing: { y = 2x − 3 −6x + 3y = −9 7 Solve the system by graphing: { 3x + y = −1 2x + y = 0 8 A father's age is three times his son's age. In five years, the father will be twice as old as the son. Write the algebraic equations to represent this situation and find their current ages. 9 Solve the equations x + 2y - 4 = 0 and 2x + 4y - 12 = 0 graphically. 10 The cost of 5 pens and 7 pencils is Rs. 50 whereas the cost of 7 pens and 5 pencils is Rs. 65. Represent the given word problem in linear equations form. Page 1 Email: Phone No: Website:
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