188
The difference between two numbers is 12. The greater number is 6 less than twice the smaller one.
(i) Representing the above situation, frame two linear equations in two variables.
(ii) Show that the equations have unique solution.
(iii) Solve the equations and hence find the numbers.
(i) Representing the above situation, frame two linear equations in two variables.
(ii) Show that the equations have unique solution.
(iii) Solve the equations and hence find the numbers.
Show SolutionHide Solution↓
Solution: (a) (i) Let the larger number be $x$ and smaller number be $y$
$x - y = 12$ (1 Mark)
$x - 2y = -6$ (1 Mark)
(ii) $\frac{a_1}{a_2} = \frac{1}{1}$ and $\frac{b_1}{b_2} = \frac{-1}{-2}$ (1 Mark)
$\frac{1}{1} \neq \frac{-1}{-2} \Rightarrow$ equations have unique solution. (1 Mark)
(iii) Solving the above equations to get $x = 30$ $y = 18$ (1+1 Marks)
$x - y = 12$ (1 Mark)
$x - 2y = -6$ (1 Mark)
(ii) $\frac{a_1}{a_2} = \frac{1}{1}$ and $\frac{b_1}{b_2} = \frac{-1}{-2}$ (1 Mark)
$\frac{1}{1} \neq \frac{-1}{-2} \Rightarrow$ equations have unique solution. (1 Mark)
(iii) Solving the above equations to get $x = 30$ $y = 18$ (1+1 Marks)