Solve Algebraic Equations with Two Variables

Graphically, the pair of equations 6x – 3y + 10 = 0 , 2x – y + 9 = 0 represents two lines which are

• intersecting at exactly one point
• intersecting at exactly two points.
• coincident. 
•  parallel.

The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have  

•  a unique solution
• exactly two solutions
• infinitely many solutions
• No solution

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

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

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is 

• –5/4
• 2/ 5 
• 15/4
• 3/2

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

• No  solution
• Infinite many solution
• Unique solution

How many solutions does this system of equations have?

• One Solution
• No solution
• Infinitely Many Solutions
• Two Solutions

There are 50 donkeys and chickens on a far.  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

This system has _____ solutions

• 0
• 1
• 2
• Infinitely many

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450
• 3x + 2y = 450
  2x + 4y = 315
• 2x + 2y = 315
  3x + 4y = 450

The solution to a system of inequalities is graphed. Which system shows this graph?

• { y < 2x + 2

  { y < x

• { y < 2x

  { y < x

• { y < x - 2

  { y > - x

• { y < 2x + 2

  { y > - x