Solve the pair of linear equations graphically: 3 x - 2 y = 1 ; 2 x + y = - 4 .

Given pair of linear equations are 3 x - 2 y = 1 and 2 x + y = - 4 . Steps for drawing each graph: ∙ Make the subject of formula as y . ∙ Choose three values for x and find the corresponding values of y . ∙ Display the values of x and y in a table. ∙ Plot the points and draw the graph. Now, 3 x - 2 y = 1 ⇒ 2 y = 3 x - 1 ⇒ y = 3 x - 1 2 x - 1 1 3 y = 3 x - 1 2 - 2 1 4 2 x + y = - 4 x - 2 - 1 0 y = - 2 x + 4 0 - 2 - 4 Now, plot the points of each equation to obtain the graphs as two straight lines. The two straight lines intersect at the point - 1 , - 2 which is the solution of the given pair of linear equations, where x = - 1 and y = - 2 . Thus, we solved the given pair of linear equations graphically.

Solve the pair of linear equations: x 3 - y 2 = 2 ; x 5 - y 2 = 1 3 5 graphically.

Given pair of linear equations are x 3 - y 2 = 2 and x 5 - y 2 = 1 3 5 . Steps for drawing each graph: ∙ Make the subject of formula as y . ∙ Choose three values for x and find the corresponding values of y . ∙ Display the values of x and y in a table. ∙ Plot the points and draw the graph. x 3 - y 2 = 2 ⇒ y 2 = x 3 - 2 ⇒ y = 2 x - 6 3 x - 3 0 3 y = 2 x - 6 3 - 6 - 4 - 2 x 5 - y 2 = 1 3 5 ⇒ y 2 = x 5 - 8 5 ⇒ y = 2 x - 8 5 x - 2 3 8 y = 2 x - 8 5 - 4 - 2 0 Now, we need to plot the points of each equation and join them. We obtained a pair of straight lines as the graphs of the pair of linear equations. The point of intersection is the solution of the given pair of equations. Hence, we solved the pair of linear equations graphically and the solution is 3 , - 2 .

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ICSE Skills In Mathematics>Algebra>Chapter 21 - Coordinate System and Graphs>EXERCISE 21(C)

V K Raman and S N Sharma Solutions for Exercise 3: EXERCISE 21(C)

Author:V K Raman & S N Sharma

V K Raman Mathematics Solutions for Exercise - V K Raman and S N Sharma Solutions for Exercise 3: EXERCISE 21(C)

Attempt the practice questions from Exercise 3: EXERCISE 21(C) with hints and solutions to strengthen your understanding. ICSE Skills In Mathematics solutions are prepared by Experienced Embibe Experts.