Solve the following systems of equations graphically:
$2 x+3 y=4$
$x-y+3=0$
The given equations are:
$2 x+3 y=4$ $.(i)$
$x-y+3=0$ ..(ii)
Putting $x=0$ in equation $(i)$, we get:
$\Rightarrow 2 \times 0+3 y=4$
$\Rightarrow y=4 / 3$
$x=0, \quad y=4 / 3$
Putting $y=0$ in equation $(i,$, we get:
$\Rightarrow 2 x+3 \times 0=4$
$\Rightarrow x=2$
$x=2, \quad y=0$
Use the following table to draw the graph.
Draw the graph by plotting the two points $A(0,4 / 3)$ and $B(2,0)$ from table
Graph of the equation....(ii):
$x-y=-3$ .(ii)
Putting $x=0$ in equation (ii) we get:
$\Rightarrow 0-y=-3$
$\Rightarrow y=3$
$x=0, \quad y=3$
Putting $y=0$ in equation $(i i)$, we get:
$\Rightarrow x-0=-3$
$\Rightarrow x=-3$
$x=-3, \quad y=0$
Use the following table to draw the graph.
Draw the graph by plotting the two points $C(0,3)$ and $D(-3,0)$ from table
The two lines intersect at points $P(-1,2)$.
Hence, $x=-1$ and $y=2$ is the solution.
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