Solving Systems of Equations

Determine the solution of the system graphed below. 

• (2, 2)
• (-2, 2)
• (2, -2)
• (-2, -2)

The solution to a system of equations is _________________. 
I.  the sum of the slopes of two lines  
II. the point where two lines intersect
III. always unique
IV. the ordered pair that makes both equations true 

• only II
• both I and II
• only IV
• both II and IV

If two equations in a linear system have the same slope and the same y-intercepts, the system will have _________________________. 

• one solution
• no solution
• many solutions
• two solutions

A system of equations is shown.  
2x + 4y = 8  
x + 2y = 4  
Which statement about the ordered pair (-2, 3) is true?

• It is the only solution to the system of equations.
• It is one of many solutions to the system.
• It is not a solution to either equation.
• It is a solution to the first equation but not the second equation.

The graph of a system of equations is shown below.  Which system of equations represents the graph?

• y = 2x – 5 and 2x + 4y = 8
• y = 3x – 5 and 2x + 4y = 8
• y = 3x – 5  and 4x + 2y = 8
• y = 2x – 5 and 4x + 2y = 8

When solved graphically, which system of equations will have infinitely many solutions?

• y = -2x + 10
  y= 4x + 3
• y = 0.5x + 5
  y = ½x + 2
• y = x + 4
  2y = 2x + 8
• y = -x + 5
  y + 2 = x

One equation in a system of equations is y = 2x + 10. Which equation below would have to be the second equation so that the system has infinitely many solutions?

• y = 5x – 8
• y = 2x – 10
• y + 2x = 10
• y = 2(x+5)

One equation in a system of equations is given in the graph. Which equation below would have to be the second equation so that the system has no solutions?

• 2x + 3y = 0
• 2x + 3y = 6
• 2x – 3y = 9
• y = 3x + 2

What is the slope-intercept form for each equation in this system? Compare the slopes and y-intercepts to describe the graph of the system. 
 3x - 4y = 28   4x + 10y = 20

• y = ¾x - 7; y = -⅖x + 2; one line
• y = ¾x - 7; y = -⅖x + 2; parallellines
• y = ¾x - 7; y = ⅖x + 2; intersecting lines
• y = ¾x - 7; y = -⅖x + 2; intersecting lines

Which system of equations has no solution? 

• y = 4x + 8
  y = 3x + 5
• 2x +5y = 10
  2x + 5y = 16 
• y = 2x + 5
  y - 2x = 5
• y = 2x - 3
  4x - 2y = 6