Question

Solve graphically the equations: - 2x – y = 1; x + 2y = 8.

Answer 1

Hint: First of all draw the graph of the two linear equations. Select the first equation and substitute x = 0 to find the value of y, substitute y = 0 and find the value of x. Join the two points to form the straight line. Similarly, draw the graph of the second equation using the same procedure. Observe the point of intersection of the two lines on the graph to get the answer.

Complete step-by-step answer:
Here we have been provided with two equations: - 2x – y = 1; x + 2y = 8 and we are asked to solve them graphically. First we need to draw the graph of the two equations. We can see that the given equations are linear in nature so their graph will be a straight line. To draw the graph of a straight line we need at least two points.
(1) Let us consider the equation 2x – y = 1.
Substituting x = 0 we get,
$\begin{align}
  & \Rightarrow -y=1 \\
 & \Rightarrow y=-1 \\
\end{align}$
Substituting y = 0 we get,
$\begin{align}
  & \Rightarrow 2x=1 \\
 & \Rightarrow x=\dfrac{1}{2} \\
\end{align}$
Therefore, the two points are $A\left( 0,-1 \right)$ and $B\left( \dfrac{1}{2},0 \right)$.
(2) Let us consider the equation x + 2y = 8.
Substituting x = 0 we get,
\[\begin{align}
  & \Rightarrow 2y=8 \\
 & \Rightarrow y=4 \\
\end{align}\]
Substituting y = 0 we get,
$\Rightarrow x=8$
Therefore, the two points are $C\left( 0,4 \right)$ and $D\left( 8,0 \right)$.
Now, let us draw the graph of the two lines and assume that the intersection point is E, so we have the graph shown below.

From the above graph we can see that the point of intersection of the two lines is given as E (2, 3). Hence, the solution of the given system of equations is x = 2 and y = 3.

Note: Note that you can check the answer by solving the given system of equations algebraically either by using the elimination method or the substitution method. It is necessary to find two points to form a straight line. You can also substitute the values of x and y other than 0 to find the two points but in that case you may have to perform some calculations so it is better to substitute 0.