suppose you ca work a total of no more than 20 hours per week at your 2 jobs. baby-sitting $5 per hour, and your cashier job pays $6 per hour. you need to earn at least $90 per week to cover your expences. question : write a system of inequalities that showas the various numbers of hours you can work at each job. Graph the result. how do you do this??

Ax+By=C

A=5,
B=6,
C=90,
So, put in the numbers to variables:
5x+6y=90.
6y=90-5x
y=15-*5over6*x
and then graph the line...

Hope I helped! :) good luck

To write a system of inequalities that shows the various numbers of hours you can work at each job, we will first define two variables:

Let x be the number of hours worked as a babysitter.
Let y be the number of hours worked as a cashier.

Now let's set up the inequalities based on the given conditions:

1. Total hours worked should not exceed 20 hours per week:
x + y ≤ 20

2. The amount earned as a babysitter ($5 per hour) multiplied by the number of hours worked should be greater than or equal to the required expenses ($90 per week):
5x ≥ 90

3. The amount earned as a cashier ($6 per hour) multiplied by the number of hours worked should also be greater than or equal to the required expenses ($90 per week):
6y ≥ 90

These three inequalities represent the constraints for the number of hours worked as a babysitter (x), the number of hours worked as a cashier (y), and the total hours worked.

To graph the result, we need to convert these inequalities into slope-intercept form (y = mx + b) and plot them on a graph. However, given the specific constraints of this problem, it is easier to create a table to represent the possible combinations and then plot the points.

We can start by creating a table of possible combinations of hours worked for each job:

| Hours as Babysitter (x) | Hours as Cashier (y) |
|-------------------------|---------------------|
| 0 | 0 |
| 1 | 19 |
| 2 | 18 |
| ... | ... |
| 18 | 2 |
| 19 | 1 |
| 20 | 0 |

Next, calculate the amount earned for each combination:

| Hours as Babysitter (x) | Hours as Cashier (y) | Amount Earned ($) as Babysitter (5x) | Amount Earned ($) as Cashier (6y) |
|-------------------------|---------------------|-------------------------------------|----------------------------------|
| 0 | 0 | 0 | 0 |
| 1 | 19 | 5 | 114 |
| 2 | 18 | 10 | 108 |
| ... | ... | ... | ... |
| 18 | 2 | 90 | 12 |
| 19 | 1 | 95 | 6 |
| 20 | 0 | 100 | 0 |

Now, plot the points on a graph where the x-axis represents the hours worked as a babysitter (x) and the y-axis represents the hours worked as a cashier (y). Shade the region that satisfies all the constraints from the given inequalities (x + y ≤ 20, 5x ≥ 90, and 6y ≥ 90).

The resulting graph will have a shaded region with points below or on the line x + y = 20, points above or on the line 5x = 90, and points above or on the line 6y = 90.

To write a system of inequalities and graph the result, we need to define the variables, set up the inequalities, and plot them on a graph.

Let's define:
x = number of hours worked as a babysitter
y = number of hours worked as a cashier

The total number of hours worked per week cannot exceed 20, so the first inequality is:
x + y ≤ 20

The earnings from babysitting ($5 per hour) and the cashier job ($6 per hour) need to be equal to or greater than $90 per week, so the second inequality is:
5x + 6y ≥ 90

To graph these inequalities, we can start by converting them into slope-intercept form (y = mx + b):

Inequality 1:
x + y ≤ 20
y ≤ -x + 20

Inequality 2:
5x + 6y ≥ 90
6y ≥ -5x + 90
y ≥ (-5/6)x + 15

To plot the graph, we need to create a coordinate plane and graph the lines.

Step 1: Draw the coordinate plane, labeling the x-axis as "Hours as Babysitter" and the y-axis as "Hours as Cashier."

Step 2: Graph Inequality 1 (y ≤ -x + 20):
- Start by finding the y-intercept, which is 20.
- Plot the point (0, 20) on the y-axis.
- Since the inequality is less than or equal to, draw a solid line through the y-intercept with a negative slope.
- Extend the line beyond the intercept on both sides.

Step 3: Graph Inequality 2 (y ≥ (-5/6)x + 15):
- Start by finding the y-intercept, which is 15.
- Plot the point (0, 15) on the y-axis.
- Since the inequality is greater than or equal to, draw a solid line through the y-intercept with a negative slope.
- Extend the line beyond the intercept on both sides.

Step 4: Shade the feasible region:
- Shade the area below the line from Inequality 1 (y ≤ -x + 20).
- Shade the area above the line from Inequality 2 (y ≥ (-5/6)x + 15).
- The shaded region is the feasible region for the number of hours worked.

The graph should show the shaded area where the inequalities overlap, indicating the various numbers of hours you can work at each job in order to earn at least $90 per week and not exceed a total of 20 hours.