Systems of Equations - Linear Equations with Two Variables

Which system of equations does NOT have the same solution as the system below?

 $3x\ +\ 5y\ =10$  

 $-x\ +4y\ =-3$  

•  $30x\ +50\ y\ =100$  
   $-10x\ +\ 40y\ =-30$  
  

•  $18x\ +30y\ =60$  
   $-6x\ +24y\ =-18$  
  

•  $6x\ +\ 10y\ =\ 20$  
   $-3x\ +12y\ =-3$  
  

•  $-15x\ -25y\ =\ -50$  
   $-\frac{1}{2}x+2y\ =-\frac{3}{2}$  
  

Which system of equations will yield the same solution as the system below?

 $x\ -\ y\ =\ 3$  

 $2x\ -\ 3y\ =\ -1$  

•  $-2x\ -\ 2y\ =\ -6$  
   $2x\ -\ 3y\ =\ -1$  
  

•  $-2x\ +\ 2y\ =\ 3$  
   $2x\ -\ 3y\ =-1$  
  

•  $2x\ -\ 2y\ =6$  
   $2x\ -\ 3y\ =-1$  
  

•  $3x\ +\ 3y\ =9$  
   $2x\ -\ 3y\ =-1$  
  

Lizzy has 30 coins that total $4.80. All of her coins are dimes, D, and quarters, Q. Which system of equations models this situation?

• $D\ +\ Q\ =\ 4.80$
  

  $.10D\ +\ .25Q\ =\ 30$
  

• $D\ +\ Q\ =\ 30$
  $.10D\ +\ .25Q\ =\ 4.80$
  

• $D\ +Q\ =30$
  $.25D\ +\ .10Q\ =\ 4.80$
  

• $D\ +\ Q\ =\ 4.80$
  $.25D\ +\ .10Q\ =\ 30$
  

How many solutions are there to the following system of equations?
 $y\ +\ 2x\ =\ 1$  
 $y\ -\ 1\ =\ -2x$  

• One Solution

• No Solution

• Infinite Solutions

How do we know if a system of equations has no solution?

• The lines are not in slope-intercept form (y=mx+b)

• The lines have the same slope and y-intercept

• The lines are perpendicular

• The lines are parallel

Tags

CCSS.8.EE.C.8A

Which system of equations has the same solution as the system below? 

 $2x+2y=16$  

 $3x-y=4$  

•  $2x+2y=16$  
   $6x-2y=8$  
  

•  $6x+6y=48$  
   $6x+2y=8$  
  

•  $x+y=16$  
   $3x-y=4$  
  

•  $2x+2y=16$  
   $6x-2y=4$  
  

What is the solution to the following system of equations?

• (-1,-1)

• (1,1)

• (1,-1)

• (-1,1)

Which of these systems has an infinite number of solutions?

• 
  

  $y=-2x+1$

  $y=-2x-3$
  

• $y=3x+4$
  $-12x+4y=16$
  

• $x+2y=10$
  $2x+4y=10$
  

• $y=2x+6$
  $4x-2y=8$
  

Tags

CCSS.8.EE.C.8B

Is (-1,5) a solution to this system of equations?

• $x+y=4$
  $x=-1$
  

• $y=-x+4$
  $y=-\frac{1}{5}x$
  

• $y=5$
  $y=x-6$
  

• $y=x+6$
  $x=2y+7$
  

Which ordered pair is the solution of the system? 

 $6x-6y=2$  

 $3x+9y=-7$  

•  $\left(\frac{2}{3},-\frac{1}{3}\right)$  

•  $\left(\frac{1}{3},\frac{2}{3}\right)$  

•  $\left(-\frac{2}{3},\frac{1}{3}\right)$  

•  $\left(-\frac{1}{3},-\frac{2}{3}\right)$  

Tags

CCSS.HSA.REI.C.9