Linear Equations

Question 19: Calculate the value of x and of y that satisfy the following simultaneous linear equations:   x + 6 y = 12 2 3 x + 2 y = 6 [4 marks] Solution: x + 6 y = 12 x = 12 − 6 y − − − ( 1 ) 2 3 x … Read more

Question 17: Solving using matrix method is not allowed in this question. Diagram shows a rectangular fish pond with the perimeter of 62 m. It is given that the length of the fish pond is 3 times its width. Calculate the length, in m, of the fish pond. Solution: Given y + 4 = 3x y … Read more

Question 14: It is given that x + 2y = 4 and x + 6y = –4. Calculate the value of x. Solution: Using Elimination method x + 2y = 4 ——– (1) x + 6y = –4 ——- (2) (1) × 3:  3x + 6y = 12 ——– (3)    x + 6y = –4 ——- (2) … Read more

6.4.4 Linear Equations, PT3 Focus Practice Question 10: It is given that 2x = 6 and 3x + y = 10. Calculate the value of y. Solution: 2x = 6 x = 3 Substitute x = 3 into 3x + y = 10 3 (3) + y = 10 y = 10 – 9 y = 1 Question … Read more

Question 7:: Solve each of the following equations: (a)  a − 2 = a 5 (b)  b − 3 4 = 2 + b 5 Solution: (a) a − 2 = a 5 5 a − 2 = a 4 a = 2 a = 2 (b) b − 3 4 = 2 + b … Read more

Question 4: Solve the following linear equations. (a) 11 + 2 x 3 = 9 (b) x − 5 3 = x 6 Solution: (a) 11 + 2 x 3 = 9 2 x 3 = 9 − 11 2 x 3 = − 2 2 x = − 6 x = − 6 2 … Read more

6.4.1 Linear Equations, PT3 Practice 1 Question 1: Solve the following linear equations.   (a)  4 – 3n = 5n – 4      (b) 4 m − 2 10 + m = 1 2   Solution: (a) 4 – 3n = 5n – 4    –3n –5n = – 4 – 4    –8n = … Read more

6.2.2  Simultaneous Linear Equations in Two Variables 1.  Two equations are said to be simultaneous linear equations in two variables if  (a) Both are linear equations in two variables, and  (b) Both involve the same variables. Example: 2x + y = 9, x = 2y + 1   2.   The solution of two simultaneous linear equations … Read more

6.2 Linear Equations   6.2.1 Linear Equations in Two Variables 1.   A linear equation in two variables is an equation which contains only linear terms and involves two variables.     2.   If the value of one variable in an equation is known, then the value of the other variable can be determined … Read more

6.1 Linear Equations   6.1.1 Equality 1. An equation is a mathematical statement that joins two equal quantities together by an equality sign ‘=’. Example: 1 km = 1000 m 2. If two quantities are unequal, the symbol ‘≠’ (is not equal) is used. Example: 9 ÷ 4 ≠ 3 6.1.2 Linear Equations in One Unknown 1. A linear … Read more