Question

solve x+y=5xy and 3x+2y=13xy

Answer 1

x+y=5xy
x=5xy-y --------(1)
putting 1 in other equation
3(5xy-y) +2y=13xy
15xy-3y+2y=13xy
y=2xy
x=1/2
y=1/3

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Answer 2

x + y = 5xy ......(1)

3x + 2y = 13xy .......(2)

Multiply (1) by 2 then we get;

2x + 2y = 10xy ......(3)

Using Elimination method for eq. (2) and (3)

3x + 2y = 13xy
2x + 2y = 10xy (change the signs)
___________
1x + 0y = 3xy
___________

$1x\:=\:3xy$ [Cancel the x on both sides]

$1\:=\:3y$

$3y\:=\:1$

$y$ = $\frac{1}{3}$

Put value of y in (1)

$x$ + $\frac{1}{3}$ = $5x$ $\frac{1}{3}$

$x$ + $\frac{1}{3}$ = $\frac{5x}{3}$

$\frac{1}{3}$ = $\frac{5x}{3}$ - $x$

$\frac{1}{3}$ = $\frac{5x\:-\:3x}{3}$

$\frac{1}{3}$ = $\frac{2x}{3}$

Now 3 of both sides are cancelled. So,

$1\:=\:2x$

$2x\:=\:1$

$x$ = $\frac{1}{2}$