Question

Graph the solution sets of the following inequalities:
\[x+2y>1\]

Answer 1

Hint: We are given an inequality and we are asked to graph the inequality given to us. We will first of all graph the equation using the equation, \[x+2y=1\], without considering the inequality now. We will put the variables equal to 0 one at a time and find the coordinates. Then, we will take a reference point and check if it follows the inequality in the expression and this check will determine the direction of the solution set of the expression either towards the reference point or away from the reference point. Hence, we will have the graph of the given inequalities.

Complete step by step answer:
According to the given question, we are given an inequality and we are asked to graph the solution set of the same.
The inequality we have is,
\[x+2y>1\]
First of all, we will plot the graph of the given equation and for plotting it we will have the equation as,
\[x+2y=1\]
We will now find points or coordinates for the same. We will put the variables equal to 0 one at a time and find the respective coordinates.
We have,
Firstly, putting \[x=0\], we get,
\[\Rightarrow 0+2y=1\]
Solving for the value of ‘y’, we get,
\[\Rightarrow 2y=1\]
\[\Rightarrow y=\dfrac{1}{2}\]
Therefore, the coordinate we obtain is, \[\left( 0,\dfrac{1}{2} \right)\]
Now, putting \[y=0\], we get,
\[\Rightarrow x+0=1\]
\[\Rightarrow x=1\]
The coordinate we obtain is, \[\left( 1,0 \right)\]
We get the graph of the equation as,

Now, to find the solution set, we will take origin as the reference point and check if it goes well with the inequality, we get,
\[x+2y>1\]
\[\Rightarrow 0+0>1\]
\[\Rightarrow 0>1\]
Which is incorrect and so we have the solution set away from the origin and so we get,

Note: The plotting of the graph should be devoid of any inequalities as it might lead to erroneous graphs of the given equation. Only after plotting the graph, the inequality in the given equation should be considered and the reference point taken can be any point except the points of the given equation and accordingly is substituted and the direction of the solution set of the equation is determined.