Question

Solve the equations using graphical method: $x+y=7$ and $2x-3y=9$

• A. $(6,-1)$
• B. $(-6,1)$
• C. $(6,1)$
• D. $(-6,-1)$

Answer 1

The correct option is C $(6,1)$

For line $2x-3y=9$

$x$	$0$	$6$
$y$	$-3$	$1$

For line $x+y=7$

$x$	$5$	$2$
$y$	$6$	$1$

$x+y=7$ ----- (1)
$2x-3y=9$ ----- (2)
From equation (1)
$y=7-x$ ------ (3)
Assume the value of $x=5,$6 and put those values in equation (3)
If $x=5,y=7-5=2$
If $x=6,y=7-6=1$

Now plotting (5, 2), (6, 1) and joining them, we get a straight line.
From equation (2),
$2x-3y=9$
$y=\frac{2x-9}{3}$ ------ (4)
Assume the value of $x=0,6$ and put those values in equation (4)

If $x=0,y=\frac{2x-9}{3}=\frac{2\left(0\right)-9}{3}=\frac{-9}{3}=-3$

If $x=6,y=\frac{2\left(6\right)-9}{3}=\frac{12-9}{3}=\frac{3}{3}=1$

Plotting $(0,-3),(6,1)$ and joining them, we get another straight line.
These lines intersect at the point $(6,1)$ and therefore the solution of the equation is $x=6,y=1$ .