Linear Equations Two Variables

A solution to a

system of linear equations

with two variables

is written as an ordered pair

( x, y ).

• True

• False

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 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

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

?

Mathematical Equivalence

OFF

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

A solution to a system

of two linear equations

in two variables

must make BOTH

equations TRUE.

• False

• True

For what values of a and b does the following pair of equations have an infinite numbers of solutions. 2x+3y=7, a(x+y)-b(x-y)=3a+b-2

• a = 5, b = - 1

• a = - 5, b = 5

• a = 5, b = 1

• a = 1, b = 5

For what value of k will pair of equations have no solution? 3x+y=1 , (2k-1)x+(k-1)y=2k+1

• 1

• 2

• 3

• 4

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

• intersecting lines

• parallel lines

• skew lines

• intersecting lines