Question

Draw the graphs of the following equations on the same graph paper:
 $\begin{align}
  & 2x+3y=12 \\
 & x-y=1 \\
\end{align}$

Answer 1

Hint: Draw the graph of the two given equations. To draw the graph of a straight line, we need at least two points. So, choose one of the equations and substitute x = 0, determine y, then substitute y = 0, determine x. Now, apply the same process for the second equation. Plot the graph of the two equations using the points obtained.

Complete step-by-step answer:
Let us assume the two equations as:
$\begin{align}
  & 2x+3y=12..................(i) \\
 & x-y=1........................(ii) \\
\end{align}$
Considering equation (i),
$2x+3y=12$
Substituting x = 0, we get,
\[\begin{align}
  & 3y=12 \\
 & \Rightarrow y=4 \\
\end{align}\]
Substituting y = 0, we get,
$\begin{align}
  & 2x=12 \\
 & \Rightarrow x=6 \\
\end{align}$
Therefore, the two points are: \[A\left( 6,0 \right)\text{ and }B\left( 0,4 \right)\].
Considering equation (ii),
\[x-y=1\]
Substituting x = 0, we get,
$\begin{align}
  & -y=1 \\
 & \Rightarrow y=-1 \\
\end{align}$
Substituting y = 0, we get,
$\Rightarrow x=1$
Therefore, the two points are: $C\left( 1,0 \right)\text{ and }D\left( 0,-1 \right)$.
Therefore, the graph of the two functions can be plotted as:
 

Note: One can also substitute the values of ‘x’ and ‘y’ other than 0 to draw the graph. The straight line will not change but only the marking of points will get changed. Generally, we substitute the value of ‘x’ and ‘y’ as 0 to make our calculation easy.