Combined Inequalities

Which point would be a solution to the system of linear inequalities?

• (8,5)

• (12,−8)

• (−8,−10)

• (−4,6)

Below are two inequalities and the graphs of their lines without the shading. By imagining where the shading should be, identify which point would satisfy BOTH inequalities.

• (10,10)

• (−5,−1)

• (8,1)

• (−3,5)

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. Is (0, 0) a solution? *You will be required to graph on the test.

Keshawn is working two summer jobs, making $25 per hour tutoring and $10 per hour landscaping. Keshawn must earn at least $100 this week. Write an inequality that would represent the possible values for the number of hours tutoring, t, and the number of hours landscaping, l, that Keshawn can work in a given week.

Use words for the inequality symbol. You will use the symbol itself on the test. Only add spaces between words.

Lauren owns a food truck that sells tacos and burritos. She only has enough supplies to make 116 tacos or burritos. She sells each taco for $3.25 and each burrito for $7.75. Lauren must sell no less than $710 worth of tacos and burritos each day. If 72 burritos were sold, determine all possible values for the number of tacos that Lauren must sell in order to meet the requirements.

Kaylee has x quarters and y dimes. She has a minimum of 18 coins worth no more than $3.60 combined. Solve this system of inequalities graphically. Is (10, 10) a solution?

You will be required to graph this question on the test.

Juan and his children went into a restaurant that sells drinks for $2 each and tacos for $4 each. Juan has $40 to spend and must buy a minimum of 11 drinks and tacos altogether. If x represents the number of drinks purchased and y represents the number of tacos purchased, write an inequality to represent the number of drinks and tacos.

Use words for the inequality symbol. You will use the symbol itself on the test. Only add spaces between words.

Cai and his children went into a movie theater and will buy drinks and candies. Each drink costs $4 and each candy costs $5. Cai has a total of $85 to spend on drinks and candies. Write an inequality that would represent the possible values for the number of drinks purchased, d, and the number of candies purchased, c.

Use words for the inequality symbol. You will use the symbol itself on the test. Only add spaces between words.

Graph and identify a possible solution.
y>-⅔x-3
y<⅔x+1

• (-3,-4)

• (3,-2)

• (4,5)

• (0,-4)

Graph and identify a possible solution.
y≥2x+3
y≥1/3x-2

• (3,3)

• (-1,-1)

• (-3,3)

• (-4,-4)