# 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) $3=2 x+y$.

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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,

Updated on 10-Oct-2022 13:40:03