9M2T3 Systems of Equations and Inequalities

At a local high school, a student ticket to a soccer game costs $5 and an adult ticket to a soccer game costs $10. For one soccer game, the amount earned on ticket sales was $1,430. Let x represent the number of student tickets sold and y represent the number of adult tickets sold. Determine the x- and y-intercepts. Which graph represents this situation?

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Samuel pays $59.99 plus $0.25 for each minute over 450 minutes for his cell phone plan. Monica pays $64.99 plus $0.10 for each minute over 450 minutes for her cell phone plan. Which system of equations represents this situation? Let x represent the number of minutes over 450.

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Solve this system of equations:

 $3x+4y=18$  
 $6x-2y=6$  

• (2, 3)
  

• (3, 2)

• (-2, -3)

• (-3, -2)

Jonathon and Raymond earn a base salary plus commission. Jonathon earns $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathon and Raymond need to sell in order to earn the same amount each month?

• $60

• $6000

• $21,000

• $54,000

Solve this system of equations:
 $2x+6y=36$  

 $4x-9y=-12$  

• (-4, 6)

• (-6, 4)

• (4, 6)

• (6, 4)

How many solutions does this system have?
 $y=7-4x$  

 $y=-2\left(2x+4\right)$  

• 0

• 1

• 2

• infinitely many

A phone company has two long distance calling plans. The first plan is $25 per month for unlimited long distance calling. The second plan is $10 per month plus $0.05 per minute of long distance calling. After how many minutes of long distance calls will it be cheaper for a customer to purchase the first plan?

• 100

• 150

• 300

• 500

Marli has $1200 in her savings account. She wants at least y in her account at the end of the year. She withdraws $150 each month. Which inequality represents this situation, where x is the number of months?

• $1200+150x\ge y$

• $1200+150x\le y$

• $1200-150x\ge y$

• $1200-150x\le y$

Curb Side Taxi charges a flat rate of $2.25 plus $0.50 per mile. Taxi-4-You charges a flat rate of $1.25 plus $0.75 per mile. Nicole has no more than y dollars to spend on a tax ride. Which system of inequalities can be used to determine the better deal? Let x represent the number of miles.

• $y>1.25x+0.75$
  

  $y>2.25x+0.5$
  

• $y<2.25+0.5x$
  $y<1.25\ +0.75x$
  

• $y\ge2.25+0.5x$
  $y\ge1.25+0.75x$
  

• $y\le2.25x+0.5$
  $y\le1.25x+0.75$
  

Which shows the solution to the system of linear inequalities?
 $y\le x+5$  
 $y\ge-x+2$  
 $y\ge3x+4$  

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