Solve the system of equations graphically: 3 x+2 y=4 2 x-3 y=7

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Solve the system of equations graphically:
3 x+2 y=4
2 x-3 y=7

Solve the system of equations graphically:
3 x+2 y=4
2 x-3 y=7

Solution:

Draw a horizontal line on a graph paper X’OX and a vertical line YOY’ representing the xaxis and $y$ -axis, respectively.
Graph of $3 x+2 y=4$
$3 x+2 y=4$
$\Rightarrow 2 y=(4-3 x)$
$\Rightarrow y=\frac{4-3 x)}{2}\dots \dots(i)$

Putting $x=0$ , we obtain $y=2$
Putting $x=2$ , we obtain $y=-1$
Putting $x=-2$ , we obtain $y=5$
Therefore, we have the following table for the equation $3 x+2 y=4$

$\begin{tabular}{|r|r|r|r|} \hline $\mathrm{x}$ & 0 & 2 & $-2$ \\ \hline $\mathrm{y}$ & 2 & $-1$ & 5 \\ \hline \end{tabular}$

So now, plot the points $\mathrm{A}(0,2), \mathrm{B}(2,-1)$ and $\mathrm{C}(-2,5)$ on the graph paper. Join $\mathrm{AB}$ and $\mathrm{AC}$ to get the graph line $\mathrm{BC}$ . Extend it on both ways.

Therefore, BC is the graph of $3 \mathrm{x}+2 \mathrm{y}=4$
Graph of $2 x-3 y=7$
$\begin{array}{l} 2 x-3 y=7 \\ \Rightarrow 3 y=(2 x-7) \\ \Rightarrow y=\frac{2 x-7}{3}\dots \dots(ii) \end{array}$

Putting $x=2$ , we obtain $y=-1$
Putting $x=-1$ , we obtain $y=-3$
Putting $x=5$ , we obtain $y=1$

Therefore, we have the following table for the eq. $2 \mathrm{x}-3 \mathrm{y}=7$

$\begin{tabular}{|r|r|r|r|} \hline $\mathrm{x}$ & 2 & $-1$ & 5 \\ \hline $\mathrm{y}$ & $-1$ & $-3$ & 1 \\ \hline \end{tabular}$

Now, plot the points $\mathrm{P}(-1,-3)$ and $\mathrm{Q}(5,1)$ . The point $\mathrm{C}(2,-1)$ has already been plotted. Join PB and QB and extend it on both ways.
As a result, line $\mathrm{PQ}$ is the graph of $2 \mathrm{x}-3 \mathrm{y}=7$