Solving Systems of Equations

How many types of solutions can a system of linear equations have?

• one

• two

• three

• four

What does a system with one solution look like on a graph?

• parallel lines

• intersecting lines at one point

• overlapping lines

• non-intersecting lines

How can we verify the solution of a linear system algebraically?

• By multiplying the equations

• By substituting the solution into the equations

• 
  By adding the equations

• By graphing the equations

What is the result of substituting the solution into both equations of a system with one solution?

• No outcome

• An undefined outcome

• The same outcome for both equations

• Different outcomes for each equation

What characterizes a linear system with no solution?

• The lines are parallel and do not intersect.

• The lines are perpendicular.

• The lines are identical and overlap completely.
• The lines intersect at one point.

Why do parallel lines indicate no solution in a linear system?

• they never intersect

• they intersect at one point

• they are the same line

• they intersect at many points

How can you adjust an equation to get it into y = mx + b form?

• By adding to the coefficient of y

• By subtracting from the coefficient of y

  
  

• 
  By dividing by the coefficient of y

• By multiplying by the coefficient of y

What encourages the system to have no solution?

• intersecting at multiple points

• having the same slope

• intersecting at one point

• having different slopes

What does it mean for a linear system to have infinitely many solutions?

• the lines intersect at one point

• the lines are parallel

• the lines intersect at two points

• the lines overlap completely

How can you graphically represent a system with infinitely many solutions?

• Graph the equations and show that they intersect at a single point.
• Graph the equations and display them as two parallel lines.
• Graph the equations and indicate that they have no solutions.
• Graph the equations and show that they overlap as a single line.