Question

find four different solutions of the equation x+2y=6

Answer 1

1-x=6-2y
2-2y=6-x
3-x-y=6-2
4-x+2=6/y

Answer 2

$\bf\underline {꧁༺Question ༻꧂}$

$\bold{find \: four \: different \: solutions \: of \: the \: equation \:x + 2y = 6.}$

$\bf\underline {꧁༺Answer༻꧂}$

$\bf\ \: By\:inspection,x=2,y=2\:is\:a\:solution\:because\:for\:x=2,y=2 \\ \bf \ x+2y=2+4=6$

$\bf \: Now,let \: us \: choose \: x=0. With \: this \: value \: of \: x, the \: given \: equation \: reduces \: to \:2y=6 \: which \: has \: the \: unique \: solution \: y=3.So \: x=0,y=3 \: is \: also \: a \: solution \: x+2y=6.Similarly, taking \: y=0,the \: given \: equation \: reduces \: to \: x=6.So,x=6,y=0 \: is \: a \: solution \: of x+2y=6 \: as \: well.Finally, let \: us \: take \: y=1. The \: given \: equation \: now \: reduces \: to \: x+2y=6, whose \: solution \: is \: given \: by \: x=4. Therefore,(4,1) \: is \: also \: solution \: of \: the \:given \: equation.So \: four \: of \: the \: infinitely \: many \: solutions \: of \: the \: given \: equation \: are:$

$\bf(2,2),(0,3),(6,0),(4,1)$