Question

If (x, y) is the solution of system of linear equations 4/x +5/y=9 7/x-8/y=-1then the value of (2x – y) is equal to

Answer 1

Given the linear equations:

$\dfrac{4}x +\dfrac{5}y=9 \\\dfrac{7}x-\dfrac{8}y=-1$

$(x,y)$ is the solution of the system of linear equations given above.

To find:

$(2x-y) = ?$

Solution:

The two given equations can be solved by making the coefficients same and then adding the coefficients of different signs.

So, let us multiply the first equation by 8 and second equation by 5.

Now, the equations become:

$\dfrac{4}x\times 8 +\dfrac{5}y\times 8=9\times 8\\\Rightarrow \dfrac{32}x+\dfrac{40}y\times 8=72\\ \\\dfrac{7}x\times 5-\dfrac{8}y\times 5=-1\times 5\\\Rightarrow \dfrac{35}x-\dfrac{40}y=-5$

Now adding the two equations, Coefficients of $\frac{1}{y}$ are 40 and -40 respectively, so the terms will get canceled out.

$\dfrac{32}{x}+\dfrac{35}{x} = 72-5\\\Rightarrow \dfrac{67}{x} = 67\\\Rightarrow x =\dfrac{67}{67}\\\Rightarrow \bold{x = 1 }$

Putting value of $x$ in 1st equation.

$\dfrac{4}1 +\dfrac{5}y=9\\\Rightarrow \dfrac{5}y=9-4\\\Rightarrow y =\dfrac{5}5\\\Rightarrow \bold{y=1}$

Hence, the required value is:

$(2x-y) = 2 \times 1 -1\\\Rightarrow 2-1 = \bold{1}$