Find four different solutions of the equation $x + 2y = 6.$
Find four different solutions of the equation $x + 2y = 6.$
By inspection, $x=2,\, y=2$ is a solution because for $x=2,\, y=2$
$x+2 y=2+4=6$
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 of $x + 2y = 6$. 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 $x + 2 = 6$, whose solution is given by $x = 4$. Therefore, $(4,\, 1)$ is also a solution of the given equation. So four of the infinitely many solutions of the given equation are :
$(2,\,2)$, $(0,\,3)$, $(6,\,0) $ and $ (4,\,1)$
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