Add and Multiply Linear Equations Graphically

Definition: one equation can be manipulated algebraically to get the other one; infinitely many solutions; graphically on the same line

• dependent equations

• solution

• dependent systems

• dependent variable

Which equation matches the table?

• y = 3x + 9

• y = x + 9 

• y = x + 3

• y = 12x - 3

• y = 5x
• y = x + 5
• y = x + 470
• y = 94x 

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

Identify the nature of solution from the graph given.

• Consistent and unique solution

• Inconsistent : No solution

The pair of equations x = a and y = b graphically represents lines which are  

• parallel 

•  intersecting at (b, a)

•  coincident

•  intersecting at (a, b)

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

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 pair of linear equations:
 kx + 4y = 5 ; 3x + 2y = 5
 is consistent only when:

• k ≠ 6

• k = 6

• k ≠ 3

• x = 3