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How many solutions does a linear inequality in two variables have?

Last updated date: 17th Jul 2024
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Hint: From the question given, we have been asked to find the number of solutions of a linear inequality in two variables. We will assume a linear inequality in two variables and find its solutions and analyse them.

For example: If apples cost $40$rupees per kilo and pears cost $53$ rupees per kilo, what combination of apples and pears can I buy with at most $1000$ rupees?
If I buy $a$ kilos of apples and $p$ kilos of pears then I spend $40a$ apples and $53p$ on pears. So, there will be $40a+53p$ in total. So, whatever combination I buy, it must satisfy
$40a+53p\le 1000$
Therefore, the solution of a linear inequality in two variables like $Ax+By > c$ is an ordered pair $\left( x,y \right)$ that produces a true statement when the values of $x$ and $y$ are substituted into the inequality.