Question

2/x+3/y = 13 ; 5/x - 4/y =-2 ​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

We have two Equation 2/x +3/y = 13 & 5/x -4/y= -2

How to solve?

step 1: First convert the whole Equation from fractional into simplest form.

Step 2: Now,the equation is in simplest form.Now, we solve it through either elimination method or through substitution method.

We solve it through substitution method

Let 1/x be 'u' and 1/y be 'v'

➙2u+3v=13------(1)

➙5u-4v= -2

from equation 1

2u +3v= 13

u=( 13-3v)÷2 ----(2)

From equation 2

➙5u-4v= -2

➙5(13-3v)/2 -4v=-2

➙65-15v/2-4v= -2

➙65-15v-8v/2=-2

➙65-23v= -4

➙-23v= -4-65

➙-23v= -69

➙v = 69÷ 23

➙v= 3

Put v = 3 into Equation 2

➙u=( 13-3v)÷ 2

➙u= (13-3(3))÷2

➙u=( 13-9)÷2

➙u= 4÷2

➙u= 2

Hence,u= 2 & v= 3

We have let 1/x = u and 1/y= v

➙1/x= 2

➙1= 2x

➙x= 1/2

➙1/y= 3

➙1=3y

➙y= 1/3

Therefore, x = 1/2 and y = 1/3

Check:

➙2/x+3/y=13

➙2÷1/2+3÷1/3

➙2×2+3×3

➙4+9= 13

Since,LHS = RHS (Verified)