Question

Solve the equations: $x-y=-1$ and $2y+3x=12$ using graphical method.

• A. $(1,-2)$
• B. $(2,3)$
• C. $(3,3)$
• D. $(-1,-2)$

Answer 1

The correct option is B $(2,3)$

$x-y=-1$ ----- $\left(1\right)$

$2y+3x=12$ ----- $\left(2\right)$

From equation $\left(1\right)$ assume the value of $x$ and $y$ to satisfy the equation to zero.

$x-y+1=0$ ------- $\left(3\right)$

Put $x=2,y=3$ in equation $\left(3\right)$

$2-3+1=0$

$-1+1=0$

$0=0$

Again put $x=4,y=5$ in equation $\left(3\right)$

$4-5+1=0$

$-1+1=0$

$0=0$

Now plotting $(2,3),(4,5)$ and joining them, we get a straight line.

From equation $\left(2\right)$ assume the value of $x$ and $y$ to satisfy the equation to zero.

$2y+3x-12=0$ ----- $\left(4\right)$

Put $x=2,y=3$ in equation $\left(4\right)$

$2\left(3\right)+3\left(2\right)-12=0$

$6+6-12=0$

$12-12=0$

$0=0$

Again put $x=4,y=0$ in equation $\left(4\right)$

$2\left(0\right)+3\left(4\right)-12=0$

$0+12-12=0$

$12-12=0$

$0=0$

Plotting $(2,3),(4,0)$ and joining them, we get another straight line.

These lines intersect at the point $(2,3)$ and therefore the solution of the equation is $x=2,y=3$ .