Choose an arbitrary amount of money to be onto your gift card.
Example Solution: 9x+y≤120 3x+8y>120 Graph:
Practice makes perfect
Let's suppose that the gift card we were given is loaded with $120. We can let x be the cost of a t-shirt and y be the cost of a sweatshirt. A situation in which we are able to buy 9 t-shirts and 1 sweatshirt can be written as an inequality.
9x+y≤120
Notice that we can afford things that total to less than or equal to the amount on the gift card. Conversely, a situation where we are unable to purchase 3 t-shirts and 8 sweatshirts can be written as the following inequality.
3x+8y>120We cannot afford a purchase that totals to more than the value of our gift card. Combining these inequalities, we get the following system.
9x+y≤120 3x+8y>120
To graph this system we need to first create boundary lines by writing the inequalities in slope-intercept form. The first inequality already has a coefficient of 1 for y, so we can simply subtract 9x from both sides.
9x+y≤120 ⇒ y≤-9x+120
Now let's solve the second inequality for slope-intercept form.
Having two of the inequalities in the slope-intercept form, we can write our system.
y≤-9x+120 y>- 38x+15
Next, we can graph our boundary lines. Remember that the first inequality will have a solid line and the second will have a dashed line.
The overlapping area shows us the possible price combinations of t-shirts x and sweatshirts y such that we could purchase 9 t-shirts and 1 sweatshirt but we could not purchase 3 t-shirts and 8 sweatshirts. To view only the solution set for the system, we can cut away the non-overlapping area.
Keep in mind that this is just one possible solution to this problem.
