Solve question 10 of this book the lesson is simultaneous linear equation

Solve question 10 of this book the lesson is simultaneous linear equation solve the following linear equations: 4x-11y -26 5. 7m 6.2 9m -2.4 11 9.3x+8y- II -z 2x + 9y 10 2. 5x+6y-14 6. 0.4* +0.7y-6.65 0.34y-43 Word Problems based on Simultaneous Linear Equations lhe following steps are used in solving word problems related to linear equations in two variables. L Assume the variables to be the unknown quantity.

Dear Student,

Please find below the solution to the asked query:

We have : $\frac{7}{x} + \frac{12}{y} = \frac{15}{2} \mathrm{and} \frac{13}{x} - \frac{9}{y} = \frac{7}{2}$ , So

We assume : $\frac{1}{x} = m \mathrm{and} \frac{1}{y} = n$ and get our equations , As:

7 m  +  12 n  = $\frac{15}{2}$ ,

14 m  + 24 n  = 15                                                  --- ( 1 )

And

13 m  - 9 n  = $\frac{7}{2}$ ,

26 m  - 18 n  = 7                                                     --- ( 2 )

Now we multiply by 9 in equation 1 and by 12 in equation 2 and get :

126 m  + 216 n  = 135                                                  --- ( 3 )

And


312 m  - 216 n  = 84                                                     --- ( 4 )

Now we add equation 3 and 4 and get :

438 m  = 219 ,

 $$\begin{gathered} \Rightarrow m = \frac{219}{438} \\ \mathbf{\Rightarrow }\mathbf{ }\mathit{m}\mathbf{ }\mathbf{=}\mathbf{ }\frac{{\displaystyle \mathbf{1}}}{{\displaystyle \mathbf{2}}} \end{gathered}$$
Substitute that value in equation 1 and get :

14 $\times \frac{1}{2}$ + 24 n  = 15  ,

7 + 24 n  = 15 ,

24 n  = 8 ,

$$\begin{gathered} n = \frac{8}{24} , \\ \mathit{n}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{1}}{\mathbf{3}} \end{gathered}$$

But we assume : $\frac{1}{x} = m \mathrm{and} \frac{1}{y} = n$ , So we get 

x  =  2 and y  =  3                                                                ( Ans )


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