Word Problems (Set Up)
Standard form review
Systems multiple methods
Inequalities
Strategy and Concept
100
Harold bought 4 pens and 3 pencils for $10. Jake bought 2 pens and 1 pencil for $4. Write a system of equations to represent this scenario.
4x + 3y = 10
2x + 1y = 4
100
What is standard form?
ax+by=c
100
-x + 2y = -15
8x - 2y = -20
(-5, -10)
100
Is the ordered pair (-2,-2) a solution to the inequality shown on the graph? Explain.
No, the ordered pair is on a dashed boundary line, so it is not included in the solution set.
100
What strategy would you use and explain why?
14x + 2y = 26
-14x - 6y = -50
elimination because the coefficients of x will cancel out.
200
The basketball game brought in a total of $550 last night by selling a total of 75 tickets. Student tickets (s) were sold for $5 and adult tickets (a) were sold for $10. Write 2 equations to model this situation.
s + a = 75
5s + 10a = 550
200
Find the x and y Intercepts for -2x+3y=12
(-6,0) and (0,4)
200
y= 2x + 3
y= -x -6
(-3,-3)
200
Write an inequality that represents the graph.
y > 1/2x + 2
200
What strategy would you use and explain why?
-5x - 5y = 10
y = -4x -17
substitution because y is already solved for.
300
A cafe sells strawberry smoothies and banana smoothies. The cafe makes a profit of $2.25 for each strawberry smoothie and a profit of $2 for each banana smoothie that is sold. The owner of the cafe wants to make a profit of more than $90 per day from the sale of smoothies. Write an inequality that represents the number of strawberry and banana smoothies the cafe needs to sell.
2.25x + 2y >90
300
Find the x and y Intercepts for 7x-6x=-21
(-3,0) and (0, 3.5)
300
-x + 3y = -15
3x + 3y = 21
(9, -2)
300
Is the ordered pair (-3,1) a solution of the system of linear inequalities? Explain.
No, the point is on the dashed line, which means it is not included in the solution set.
300
Is there 1 solution, No solution, or Infinite solutions for the system of linear equations below? AND JUSTIFY WHY
3x - y = 19
-3x + y = 10
No Solutions because it is a false statement.
400
Charity wants to buy more than 5 items at sheetz but only has $6.50 to spend. Each candy bar cost $1 and each drink cost $1.50. Write a system of inequalities to find the number of candy bars (c) and the number of drinks (d) she bought.
c + d > 5
1c + 1.50d ≤ 6.50
400
Find the missing point using the following equation: 5x-2y=14 (2,?)
(2,-2)
400
y = -2x - 9
3x - 6y = 9
(-3, -3)
400
Write a system of linear inequalities represented by the graph:
y>=2/3x-2
y>=-3x+2
400
What is a system?
Two or more equations or inequalities
500
Andy has over 10 movies and tv episodes he wants to watch this weekend. He only is allowed to watch under 12 hours of . Each movie is 2 hours long and each show is 0.5 hours long. Write a system of inequalities to represent the situation
m + s > 10
2m + .5s < 12
500
The equation of a line has a slope that is -2 and the x-intercept is (5, 0). What is the y intercept?
(0, 10)
500
4x + 3y = -14
8x + 10y = -36
(-2, -2)
500
Write an inequality that represents the graph.
y<=2
500
Where do you find the solutions to a system of inequalities?
Where both lines are shaded