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Systems of Equations
Systems of Inequalities
Linear Equations
Linear Inequalities
Real World Problems
100
y + 4x = 8 5x + 2y = 13
What is (x, y) = (1, 4)
100
y > -3 y > x + 1 Find the slope-intercept form equation of both inequalities and the point of intercept
What is y=-3,y=x+1, (-4,-3)
100
Solve 5x + 7 = 3(x + 1).
What is x < –2
100
Solve 2x < 9.
x < 9/2
100
Katie has $50 in a savings account at the beginning of the summer. She wants to have at least $20 in the account by the end of the summer. She withdraws $2 each week for food, clothes, and movie tickets.For how many weeks can Katie withdraw money?
What is What is 15 weeks?
200
2x + 2y = 6 12 = 2y - x
What is (x, y) = (- 2, 5)
200
y ≤ 1 y ≤ 2x -3 Find the slope-intercept form equation of both inequalities and the point of intercept
What is y=1, y=2x-3, (1,2)
200
6x-24=108
What is 22.
200
2. Skate Land charges a $50 flat fee for a birthday party rental and $4 for each person. Joann has no more than $100 to budget for her party.How many people can attend Joann’s party?
What is 12 people
200
You can work a total of no more then 41 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $254 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job.
What is Hours: x + y ≤ 41 Money: 5x + 8y ≥ 254
300
2x + 2y = 4 5y - 3x = 6
What is (x, y) = (1/2,3/2)
300
y < 2x + 1 y < - 3(x - 1) Give a point in the solution set
What is in the solution set x is less than .4 and y is less than 1.8
300
2/3x+5=25
What is 30
300
Solve –2x < 5.
What is x > –5/2
300
Junebug has two jobs, babysitting, which pays $5 per hour, and bagging groceries, which pays $6 per hour. You can work no more than 20 hours each week, but you need to earn at least $90 per week. How many hours can you work at each job?
What is the possible solutions of 4 hours babysitting and 14 hours bagging groceries 10 hours babysitting and 8 hours bagging groceries 20 hours babysitting and 0 hours bagging groceries. All solutions must equal at least 90 dollars when the hours are calculated
400
10x + 7y = 49 10y - x = 70
What is (x, y) = (0, 7)
400
x + 2y≤ 8 y ≤ x + 4 Find the slope-intercept form equation of both inequalities and the point of intercept
What is y = (-1/2)x +4,y = x + 4, (0,4)
400
1/2x-5=20
What is 50
400
Solve 3(x – 2) + 4 > 2(2x – 3).
What is x < 4
400
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?
What is There were 1500 children and 700 adults.
500
4y + 2x = 5 x = 8 - 2y
What is No solutions. The system is inconsistent.
500
x + y > 2 y ≤ x Find the slope-intercept form equation of both inequalities and the point of intercept
What is y=-x+2, y=x, (1,1)
500
40+2x=194
What is x=77
500
(2x – 3)/4 < 2.
What is x < 11/2 = 5.5
500
Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She is only allowed to work 13 hours per week. She wants to make at least $65. What is the least amount of hours she can work?
What is 10 hours?