Thursday Review: Systems of Equations and Inequalities

Thursday Review: Systems of Equations and Inequalities

Let's get ready for our test!

Solve Systems with Substitution

Look for or create x= or y=

Multiple Choice

Which correctly substitutes Equation 1 into Equation 2?  

  $y=-7x-15$  

 $5x+4y=-14$  

•  $5x+4\left(-7x-15\right)=-14$  

•  $5\left(-7x-15\right)+4y=-14$  

•  $5x+4y=-7x-14$  

•  $5x-7x-15=-14$  

Multiple Choice

Currently, Ashley is 3 years older than Beth. In 5 years, Ashley will be twice as old as Beth. What equations could represent this system?

• 
  

  $x=3y$
  $x+5=2y+5$
  

• $x=y+3$
  $x+5=2\left(y+5\right)$
  

• $x+y=3$
  $x+5=2y+5$
  

• None of these.

Solving Systems with Elimination

Multiply and Add to eliminate one variable

Multiple Choice

What is the correct result of adding these two equations together? $4x+9y=-28$  
 $-4x-y=28$  

• No Solutions

•  $10y=0$  

•  $8y=0$  

•  $8x+8y=0$  

Multiple Choice

What could you multiply the first equation by to eliminate the y-variables?

 $5x-y=8$  

 $7x+3y=-2$  

• Multiply the first equation by -3

• Multiply the first equation by 3

• Multiply the first equation by 7

• Multiply the first equation by -7

Multiple Choice

You want to mix a 50% solution with a 75% solution to make 20 liters of a 60% solution. What system of equations could represent this system?

• 
  

  $x+y=20$
  

  $50x+75y=60$
  

• $x+y=20$
  $x+y=60$
  

• $x+y=20$
  $50x+75y=1200$
  

• None of these.

Solve Systems by Graphing

Find where the two lines intersect.

Multiple Choice

What is the solution to the system of equations?

• (-7, 1)

• (1, -7)

• (-7, -1)

• (-1, 7)

Multiple Choice

How many solutions does this system have?

• One Solution

• Two Solutions

• No Solutions

• Infinitely Many Solutions

Multiple Choice

When graphing, if the equations have the same slope and same y-intercept, the system will have __________.

• One Solution

• Two Solutions

• No Solutions

• Infinitely Many Solutions

Graphing Systems of Inequalities

Shading Rules:

Multiple Choice

Which ordered pair is NOT a solution?

• (4, -1)

• (6, 2)

• (3, 1)

• (3, -4)

Multiple Choice

Mr. Greenwood is making wooden duck calls and turkey calls. In one day, he can make no more than 30 calls. He profits $5 from each duck call and $7 from each turkey call. If he wants to profit at least $300 a day, what system of inequalities could help him decide how many calls to make?

• $x+y\ge30$
  $5x+7y\ge300$
  

• $x+y\le30$
  $5x+7y\le300$
  

• $x+y\le30$
  $5x+7y\ge300$
  

• $x+y\ge30$
  $5x+7y\le300$