- Home
- Standard 9
- Mathematics
समीकरण $2 x+1=x-3$ को हल कीजिए और हल को
$(i)$ संख्या रेखा
$(ii)$ कार्तीय तल पर निरूपित कीजिए।
Solution
We solve $2x + 1 = x -3$, to get
$2x -x = -3 -1$
i.e., $x = -\,4$
$(i)$ The representation of the solution on the number line is shown in Fig. $(i)$, where $x = -\, 4$ is treated as an equation in one variable.
$(ii)$ We know that $x=-\,4$ can be written as
$x+0 y=-\,4$
which is a linear equation in the variables $x$ and $y .$ This is represented by a line. Now all the values of $y$ are permissible because $0y$ is always $0 .$ However, $x$ must satisfy the equation $x=-4 .$ Hence, two solutions of the given equation are $x=-4$, $y=0$ and $x=-\,4$ $y=2$
Note that the graph $AB$ is a line parallel to the $y$ – axis and at a distance of $4$ units to the left of it (see Fig. $(ii) $).
Similarly, you can obtain a line parallel to the $x$ – axis corresponding to equations of the type
$y=3$ or $0x+1y=3$
