Question

Draw the graphs of the following equations on the same graph paper:
$2x+3y=12$
$x-y=1$

Answer 1

The given linear equations are:

$2x+3y=12$ and $x-y=1$

Let $2x+3y=12$ be $a$ and $x-y=1$ be $b$.

Solving $a$:

$2x+3y=12$

$\Rightarrow y=\frac{12-2x}{3}$

Substituting $x=0$, we get:

$y=\frac{12-2\left(0\right)}{3}=4$

and substituting $x=6$, we get:

$y=\frac{12-2\left(6\right)}{3}=0$

$\therefore (0,4)and(6,0)$ are the solutions of $a$.

Plotting these coordinates on the $xy-plane$ and joining them, we will get the line $a$.

Similarly, solving $a$:

$x-y=1$

$\Rightarrow y=x-1$

Substituting $x=0$, we get:

$y=0-1=-1$

and substituting $x=1$, we get:

$y=1-1=0$

$\therefore (0,-1)and(1,0)$ are the solutions of $b$.

Plotting these coordinates on the $xy-plane$ and joining them, we will get the line $b$.

Hence, we will obtain a graph as shown above by plotting the given linear equations on the same graph.