Question

Solve the equations: $2x+2y=4$ and $-2x+3y=1$ using graphical method.

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

Answer 1

Answer: (A)

(1, 1)

$2x+2y=4$ ----- (1)
$-2x+3y=1$ ----- (2)
From equation (1) assume the value of $x$ and $y$ to satisfy the equation to zero.
$2x+2y-4=0$------ (3)
Put $x=0,y=2$ in equation (3)
$2\left(0\right)+2\left(2\right)-4=0$
$4-4=0$
$0=0$
Again put $x=1,y=1$ in equation (3)
$2\left(1\right)+2\left(1\right)-4=0$
$4-4=0$
$0=0$
Now plotting $(0,2),(1,1)$ and joining them, we get a straight line.
From equation (2) assume the value of $x$ and $y$ to satisfy the equation to zero.
$-2x+3y-1=0$ ----- (4)
Put $x=-0.5,y=0$ in equation (4)
$-2(-0.5)+3\left(0\right)-1=0$
$1+0-1=0$
$0=0$
Again put $x=1,y=1$ in equation (4)
$-2\left(1\right)+3\left(1\right)-1=0$
$-2+3-1=0$
$-3+3=0$
$0=0$
Plotting $(-0.5,0),(1,1)$ and joining them, we get another straight line.
These lines intersect at the point (1, 1) and therefore the solution of the equation is $x=1,y=1$