Chapter 3.3, Problem 32PPSE

Solution

To solve : A system of inequalities graphically to model situations where in an entrance exam maximum marks for math and verbal session is $1600$ . for admission math score should be at least $600.$

  $\begin{array}{l}y\ge 600\\ x+y\le 1600\end{array}$

Given information:

The given statement is in an entrance exam maximum marks for math and verbal session is $1600$ . for admission math score should be at least $600.$

Concept used:

Graph each inequality and then overlapping region is the solution of the system.

Calculations:

Let $x$ be the marks for the verbal exam.

Let $y$ be the marks for math exam.

Here maximum mark for both subject is $1600$

That is $x+y\le 1600$ .

And the marks for math to get admission is at least $600.$

That is $y\ge 600.$

Then the system of the inequalities will be $\begin{array}{l}x+y\le 1600\\ y\ge 600\end{array}$ .

The graph of the inequalities is given below:

  

In the graph where overlapping region is the solution set.

To check $$ take $\left(600,1000\right)$ and check this point satisfy the inequalities.

  $\begin{array}{l}x+y\le 1600y\ge 600\\ 600+1000\le 1600600\ge 600\end{array}$

So $\left(600,1000\right)$ is true for the inequality and in the solution set.