Question

Solve the following simultaneous equations graphically.

2x + 3y = 12; x - y = 1​

Answer 1

Step-by-step explanation:

2x+3y=12

y=

3

12−2x

∣x=0,6,3∣

∣y=4,0,2∣

x−y=1

y=x−1

∣x=0,1,3∣

∣y=−1,0,2∣

Answer 2

${ \large{ \sf{ \underbrace{\underline{\bigstar \: Answer}}}}}$

$\textbf\color{pink}{2x+3y=12—(i)}$

$\textbf{x-y=1—(ii)}$

from (i)

$\textbf{2x=12-3y}$

$\textbf{x=(12-3y)/2}$

let us take three solution of this equation

1. put y=0 we get

$\textbf{x=(12-0)/2=12/2=6}$

2. put y=2 we get

$\textbf{x=(12-6)/2=6/2=3}$

3. put y=4 we get

$\textbf{x=(12-12)/2=0/2=0}$

therefore the three solutions of (i) are (6,0),(3,2) and(0,4)

Next from (ii)

$\textbf{x=(12-12)/2=0/2=0}$x=y+1

let us take three solution of this equation

1. put y=0 we get

$\textbf{x=0+1=1}$

2. put y=2 we get

$\textbf{x=2+1=3}$

3. put y=4 we get

$\textbf{x=4+1=5}$

therefore the three solutions of this equation are (1,0),(3,2) and (5,4)

When we plot these points in graph we see that the intersection point of the two lines of the euation is (3,2)

$\tt{so}$

$\tt\color{red}{the \:solution \:of\: this\: equation\: is \:x=3 \:and \:y=2}$

Done :)