# Solve the following systems of equations graphically:

Question:

Solve the following systems of equations graphically:

$x-2 y=5$

$2 x+3 y=10$

Solution:

The given equations are

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

$2 x+3 y=10 \quad \ldots \ldots \ldots($ ii $)$

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

$\Rightarrow 0-2 y=5$

$\Rightarrow y=-5 / 2$

$x=0, y=-5 / 2$

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

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

$\Rightarrow x=5$

$x=5, \quad y=0$

Use the following table to draw the graph.

Draw the graph by plotting the two points $A(0,-5 / 2)$ and $B(5,0)$ from table.

Graph the equation (ii):

$\Rightarrow 2 x+3 y=10 \ldots \ldots .(i i)$

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

$\Rightarrow 2 \times 0+3 y=10$

$\Rightarrow y=10 / 3$

$x=0, \quad y=10 / 3$

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

$\Rightarrow 2 x+3 \times 0=10$

$\Rightarrow x=5$

$x=5, \quad y=0$

Use the following table to draw the graph.

Draw the graph by plotting the two points $C(0,10 / 3)$ and $B(5,0)$ from table.

The two lines intersects at point $\mathrm{B}(5,0)$.

Hence $x=5, y=0$ is the solution