Question

Using graphical method check whether the given equation is consistent: $3x-y=4$ and $7x+2y=18$

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

Answer 1

The correct option is A $(2,2)$

$3x-y=4$ ----- (1)
$7x+2y=18$ ----- (2)
From equation (1) assume the value of $x$ and $y$ to satisfy the equation to zero.
$3x-y-4=0$ ------ (3)
Put $x=0,y=-4$ in equation (3)
$3\left(0\right)-(-4)-4=0$
$4-4=0$
$0=0$
Again put $x=2,y=2$ in equation (3)
$3\left(2\right)-\left(2\right)-4=0$
$6-2-4=0$
$6-6=0$
$0=0$
Now plotting $(0,-4),(2,2)$ and joining them, we get a straight line.
From equation (2) assume the value of $x$ and $y$ to satisfy the equation to zero.
$7x+2y-18=0$ ----- (4)
Put $x=0,y=9$ in equation (4)
$7\left(0\right)+2\left(9\right)-18=0$
$18-18=0$
$0=0$
Again put $x=2,y=2$ in equation (4)
$7\left(2\right)+2\left(2\right)-18=0$
$14+4-18=0$
$18-18=0$
$0=0$
Plotting $(0,9),(2,2)$ and joining them, we get another straight line.
These lines intersect at the point $(2,2)$ and therefore the solution of the equation is $x=2,y=2$.