Question

Solve the equations: $x-5y=15$ and $2x+5y=0$ using graphical method.

• A. (5, 2)
• B. (-5, 2)
• C. (5, -2)
• D. (-5, -2)

Answer 1

The correct option is C (5, -2)

Given equations are:

$x-5y=15$ ----- (1)
$2x+5y=0$ ----- (2)

From equation (1) assume the value of $x$ and $y$ to satisfy the equation to zero.
$x-5y-15=0$ ------ (3)
Put $x=0,y=-3$ in equation (3)
$0-5(-3)-15=0$
$15-15=0$
$0=0$

Again, put $x=5,y=-2$ in equation (3)
$5-5(-2)-15=0$
$5+10-15=0$
$15-15=0$
$0=0$
Now plotting $(0,-3),(5,-2)$ and joining them, we get a straight line.

From equation (2) assume the value of $x$ and $y$ to satisfy the equation to zero.
Put $x=5,y=-2$ in equation (2)
$2x+5y=0$
$2\left(5\right)+5(-2)=0$
$10-10=0$
$0=0$

Again, put $x=0,y=0$ in equation (2)
$2\left(0\right)+5\left(0\right)=0$
$0+0=0$
$0=0$
Plotting $(5,-2),(0,0)$ and joining them, we get another straight line.

The graph of both the equations is as shown above.

As can be seen from the graph, these lines intersect at the point $(5,-2)$ and therefore the solution of the equation is $x=5,y=-2$.

Hence, the solution of the given equations is $(5,-2)$.