# Solve the following systems of equations graphically:

Question:

Solve the following systems of equations graphically:
x + y = 3
2x + 5y = 12

Solution:

The given equations are:

$x+y=3 \quad \ldots \ldots(i)$

$2 x+5 y=12 \quad \ldots \ldots(i i)$

Putting $x=0$ in equation $(i)$, we get:

$\Rightarrow 0+y=3$

$\Rightarrow y=3$

$x=0, y=3$

Putting $y=0$ in equation $(i)$, 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 $A(0,3)$ and $B(3,0)$ from table.

Graph of the equation $(i i):$

$\Rightarrow 2 x+5 y=12 \quad \ldots \ldots .(i i)$

Putting $x=0$ in equation (ii), we get:

$\Rightarrow 2 \times o+5 y=12$

$\Rightarrow 5 y=12$

$\Rightarrow y=12 / 5$

$x=0, \quad y=12 / 5$

Putting $y=0$ in equation (ii), we get:

$\Rightarrow 2 x+5 \times 0=12$

$\Rightarrow 2 x=12$

$\Rightarrow x=6$

$x=6, \quad y=0$

Use the following table to draw the graph.

Draw the graph by plotting the two points $C(0,12 / 5), D(6,0)$ from the table.

The two lines intersect at point $\mathrm{P}(1,2)$.

Hence, $x=1$ and $y=2$ is the solution.