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Draw the graph of each of the following linear equations in two variables:
(i) $ x+y=4 $
(ii) $ x-y=2 $
(iii) $ y=3 x $
(iv) $ 3=2 x+y $.
To do:
We have to draw the graph for each of the given linear equations in two variables.
Solution:
We know that,
To draw a graph of a linear equation in two variables, we need at least two solutions to the given equation.
(i) To find the solutions to the given equation $x+y=4$.
Let us substitute $x=0$ and $y=0$ in equation $x+y=4$
For $x=0$
We get,
$0+y=4$
$y=4$
For $y=0$
We get,
$x+0=4$
$x=4$
Therefore,
$(0, 4)$ and $(4, 0)$ are two solutions of the equation$x+y=4$.
Hence,
The graph of the linear equation $x+y=4$ in two variables is,
(ii) To find the solutions to the given equation $x-y=2$.
Let us substitute $x=0$ and $y=0$ in equation $x-y=2$
For $x=0$
We get,
$0-y=2$
$y=-2$
For $y=0$
We get,
$x-0=2$
$x=2$
Therefore,
$(0, -2)$ and $(2, 0)$ are two solutions of the equation$x-y=2$.
Hence,
The graph of the linear equation $x-y=2$ in two variables is,
(iii) To find the solutions to the given equation $y=3x$.
Let us substitute $x=0$ and $y=3$ in equation $y=3x$
For $x=0$
We get,
$y=3(0)$
$y=0$
For $y=3$
We get,
$3=3x$
$3x=3$
$x=1$
Therefore,
$(0, 0)$ and $(1, 3)$ are two solutions of the equation$x+y=4$.
Hence,
The graph of the linear equation $y=3x$ in two variables is,
(iv) To find the solutions to the given equation $3=2x+y$.
Let us substitute $x=0$ and $y=1$ in equation $3=2x+y$
For $x=0$
We get,
$3=2(0)+y$
$3=0+y$
$3=y$
For $y=1$
We get,
$3=2x+1$
$3-1=2x$
$2=2x$
$x=1$
Therefore,
$(0, 3)$ and $(1, 1)$ are two solutions of the equation$x+y=4$.
Hence,
The graph of the linear equation $3=2x+y$ in two variables is,