Solving Pairs of Linear Equations in Two Variables Special Cases

If a system of equations has no solution, what does the graph look like?

• intersecting lines

• parallel lines

• coincident lines

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines
• the same line 
• Intersecting lines

If a pair of linear equations is consistent, then the lines will be 

•  parallel
• always coincident
• intersecting or coincident
•  always intersecting

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?

• 1/2
• −1/2
• 2
• −2

The equations 4x + 3y – 1 = 5 and 12x + 9y = 15 represent 

• No  solution
• Infinite many solution
• Unique solution

There are 50 donkeys and chickens on a farm. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has?

• d + c = 174

  4d + 2c = 50

• d + c = 50

  4d + 2c = 174

• d + c = 50

  2d + 4c = 174

• d + c = 174

  2d + 4c = 50

What is the solution to a system of equations?

• The point that the equations have in common.

• The point where the two lines intersect.

• All of the above.

The ordered pair that satisfies (makes them true) all equations in the system is a called a ________________.

• system of equations

• graph

• solution of a system

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

The pair of linear equations 3x + 5y = 3 ; 6x + ky = 8 do not have any solutions if : 

• k = 5
• k = 10
• k ≠ 10
• k ≠ 5