Emma and her children went into a restaurant where they sell hotdogs for $4 each and drinks for $1.50 each. Emma has $30 to spend and must buy no less than 9 hotdogs and drinks altogether. If xx represents the number of hotdogs purchased and yy represents the number of drinks purchased, write and solve a system of inequalities graphically and determine one possible solution.

6 hotdogs and 4 drinks

Step-by-step explanation:

4x + 1.50y = 30

For questions like this, you can do the equation that represents the price of the products first.

x + y   9

After that, you can write the equation that represents the quantities.

Now, you just have to graph it to find the solution. When you're graphing, make sure that y is alone on one side. Here's how you rearrange the equations:

The first equation:

4x + 1.50y =30

*Subtract 4x from both sides, which leads to:

1.50 y = -4x + 30

*Divide by 1.50 on both sides, which leads to:

y = -2.66x + 20

The second equation:

x + y   9

*Subtract x from both sides, which leads to:

y   -1x + 9

Now, use any graphing calculator (I prefer Desmos) to graph these two equations. In fact, you can just graph it on paper, too.

Here is the graph: (it is attached as a file)

You can look for any points that are on the red line but are also shaded blue. Make sure you look only in Quadrant 1- don't go into the negatives! One good point to choose would be (6,4)- this means that you buy 6 hotdogs and 4 drinks.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!