Question

Using graphical method check whether the given equation is consistent: $6x+7y=49$ and $3x+7y=28$

• A. $(7,1)$
• B. $(-7,-1)$
• C. $(-7,1)$
• D. $(7,-1)$

Answer 1

Answer: (A)

$(7,1)$

$6x+7y=49$ ----- (1)
$3x+7y=28$ ----- (2)
From equation (1) assume the value of $x$ and $y$ to satisfy the equation to zero.
$6x+7y-49=0$ ------ (3)
Put $x=0,y=7$ in equation (3)
$6\left(0\right)+7\left(7\right)-49=0$
$49-49=0$
$0=0$
Again put $x=7,y=1$ in equation (3)
$6\left(7\right)+7\left(1\right)-49=0$
$42+7-49=0$
$49-49=0$
$0=0$
Now plotting $(0,7),(7,1)$ and joining them, we get a straight line.
From equation (2) assume the value of $x$ and $y$ to satisfy the equation to zero.
$3x+7y-28=0$ ----- (4)
Put $x=0,y=4$ in equation (4)
$3\left(0\right)+7\left(4\right)-28=0$
$28-28=0$
$0=0$
Again put $x=7,y=1$ in equation (4)
$3\left(7\right)+7\left(1\right)-28=0$
$21+7-28=0$
$28-28=0$
$0=0$
Plotting $(0,4),(7,1)$ and joining them, we get another straight line.
These lines intersect at the point $(7,1)$ and therefore the solution of the equation is $x=7,y=1$.
In the above graph, the lines intersect each other at a point. In this case, the system will have exactly one solution. So, the equations are consistent.