Question

Hello I'm having difficulty with these type of problems please help

Answer 1

Step-by-step explanation:

We are given the following system of inequalities;

`\begin{gathered} -7x+5y>10 \\ x\ge10 \\ y\ge10 \end{gathered}`

We shall plot the graph of each inequality starting with the first one. Note that the quickest way to do this would be to take two endpoints. We shall take the first as;

`\begin{gathered} When\text{ }x=0 \\ -7(0)+5y=10 \\ 5y=10 \end{gathered}`
`(5y)/(5)=(10)/(5)`
`y=2`

We now have the endpoint;

`(0,2)`

Also, when y = -5;

`\begin{gathered} When\text{ }y=-5 \\ -7x+5(-5)=10 \end{gathered}`
`-7x-25=10`
`-7x=10+25`
`-7x=35`
`-(7x)/(-7)=(35)/(-7)`
`x=-5`

We also have the cordinates;

`(-5,-5)`

We can plot these two endpoints on a graph and then shade the entire region towards the left and upwards. This is because the graph represents a "greater than" inequality. Note also that the lines would be broken lines (or dashed lines) since the inequality does not include the equal to sign.

For the other inequalities;

`x\ge0`

We would have a vertical line just on point zero. The line would be a bold unbroken line. Similarly, for the other inequality;

`y\ge0`

We would have a horizontal line that lies just on the point zero. This too would be an unbroken line.

The graphs of these system of equations will now be as shown below;

ANSWER: