Answer:
Given Question
If
[tex] \sf \: \dfrac{7}{x} + \dfrac{8}{y} = 2, \: \dfrac{2}{x} + \dfrac{12}{y} = 20, \: then \: x \: = \: [/tex]
[tex] \green{\large\underline{\sf{Solution-}}}[/tex]
Given pair of equations are
[tex]\rm :\longmapsto\:\dfrac{7}{x} + \dfrac{8}{y} = 2 - - - - (1)[/tex]
and
[tex]\rm :\longmapsto\:\dfrac{2}{x} + \dfrac{12}{y} = 20[/tex]
On dividing by 2, we get
[tex]\rm :\longmapsto\:\dfrac{1}{x} + \dfrac{6}{y} = 10 - - - - (2)[/tex]
On multiply equation (1) by 3 and (2) by 4, we get
[tex]\rm :\longmapsto\:\dfrac{21}{x} + \dfrac{24}{y} = 6 - - - - (3)[/tex]
and
[tex]\rm :\longmapsto\:\dfrac{4}{x} + \dfrac{24}{y} = 40 - - - - (4)[/tex]
On Subtracting equation (3) from (4), we get
[tex]\rm :\longmapsto\: - \dfrac{17}{x} = 34[/tex]
[tex]\rm :\longmapsto\: - \dfrac{17}{34} = x[/tex]
[tex]\bf\implies \:x \: = \: - \: \dfrac{1}{2} [/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Concept Used :-
There are 4 methods to solve this type of pair of linear equations.
1. Method of Substitution
2. Method of Eliminations
3. Method of Cross Multiplication
4. Graphical Method
We prefer here Method of Eliminations :-
To solve systems using elimination, follow this procedure:
The Elimination Method
Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient.
Step 2: Subtract the second equation from the first to eliminate one variable
Step 3: Solve this new equation for other variable.
Step 4: Substitute the value of variable thus evaluated into either Equation 1 or Equation 2 and get the value other variable.
