Solve the following pair of linear equations: | vedclass

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(C) Given equations are:$(1)$ $x + y = 5xy$$(2)$ $3x + 2y = 13xy$Dividing both equations by $xy$ (assuming $x 
eq 0, y 
eq 0$):From $(1)$: $1/y + 1/

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$(0, 0), (1/2, 1/3)$

Vedclass · Answer

(C) Given equations are:$(1)$ $x + y = 5xy$$(2)$ $3x + 2y = 13xy$Dividing both equations by $xy$ (assuming $x 
eq 0, y 
eq 0$):From $(1)$: $1/y + 1/x = 5$  =>  $1/x + 1/y = 5$  --- $(3)$From $(2)$: $3/y + 2/x = 13$  =>  $2/x + 3/y = 13$ --- $(4)$Let $u = 1/x$ and $v = 1/y$. The equations become:$(3)$ $u + v = 5$$(4)$ $2u + 3v = 13$Multiply $(3)$ by $2$: $2u + 2v = 10$ --- $(5)$Subtract $(5)$ from $(4)$: $(2u + 3v) - (2u + 2v) = 13 - 10$  =>  $v = 3$Substitute $v = 3$ in $(3)$: $u + 3 = 5$  =>  $u = 2$Since $u = 1/x = 2$,$x = 1/2$.Since $v = 1/y = 3$,$y = 1/3$.Also,if $x=0$ and $y=0$,both equations are satisfied $(0=0)$.Thus,the solutions are $(0, 0)$ and $(1/2, 1/3)$.

Solve the following pair of linear equations: $x+y=5xy$ and $3x+2y=13xy$.

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