breadth by 5 units, the area will increase by 50 sq units. Find the length and breadth of therectangle.
9. In a class, if three students sit on each bench, one student will be left. If four students sit oneach bench, one bench will be left. Find the number of students and the number of benchesin that class.
4.3 ALGEBRAIC METHODS OF FINDING THE SOLUTIONS FOR A PAIR OF LINEAR EQUATIONS We have learnt how to solve a pair of linear equations graphically. But, the graphical methodis not convenient in cases where the point representing the solution has no integral co-ordinates.
For example, when the solution is of the form ( 3 , 2 7 ), (- 1.75, 3.3), (413 , 119 ) etc. There
is every possibility of making mistakes while reading such co-ordinates. Is there any alternativemethod of finding a solution? There are several other methods, some of which we shall discussnow.
4.3.1 SUBSTITUTION METHOD This method is useful for solving a pair of linear equations in two variables where onevariable can easily be written in terms of the other variable. To understand this method, let usconsider it step-wise.
step-1 : In one of the equations, express one variable in terms of the other variable. Say y interms of x.
step-2: Substitute the value of y obtained in step 1 in the second equation.
step-3 : Simplify the equation obtained in step 2 and find the value of x.
step-4 : Substitute the value of x obtained in step 3 in either of the equations and solve it for y.
step-5: Check the obtained solution by substituting the values of x and y in both the originalequations.
Example-6 Solve the given pair of equations using substitution method. 2x - y = 5
3x + 2y = 11
solution : 2x - y = 5 (1) 3x + 2y = 11 (2) Equation (1) can be written as y = 2x - 5